A system of additive functional equations in complex Banach algebras
In this article, we solve the system of additive functional equations: fx y gx gy gx y f y x fx 2 , 2 4 ⎧ ⎨ ⎩ ( ) () () ( ) ( ) () +− = +− −= and prove the Hyers-Ulam stability of the system of additive functional equations in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of...
- Autores:
-
Paokanta, Siriluk
Dehghanian, Mehdi
Park, Choonkil
Sayyari, Yamin
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2023
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
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- oai:repositorio.cuc.edu.co:11323/10522
- Acceso en línea:
- https://hdl.handle.net/11323/10522
https://repositorio.cuc.edu.co/
- Palabra clave:
- Additive mapping
F-hom-der
Fixed point method
Hyers-Ulam stability
System of additive functional equations
- Rights
- openAccess
- License
- Atribución 4.0 Internacional (CC BY 4.0)
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A system of additive functional equations in complex Banach algebras |
| title |
A system of additive functional equations in complex Banach algebras |
| spellingShingle |
A system of additive functional equations in complex Banach algebras Additive mapping F-hom-der Fixed point method Hyers-Ulam stability System of additive functional equations |
| title_short |
A system of additive functional equations in complex Banach algebras |
| title_full |
A system of additive functional equations in complex Banach algebras |
| title_fullStr |
A system of additive functional equations in complex Banach algebras |
| title_full_unstemmed |
A system of additive functional equations in complex Banach algebras |
| title_sort |
A system of additive functional equations in complex Banach algebras |
| dc.creator.fl_str_mv |
Paokanta, Siriluk Dehghanian, Mehdi Park, Choonkil Sayyari, Yamin |
| dc.contributor.author.none.fl_str_mv |
Paokanta, Siriluk Dehghanian, Mehdi Park, Choonkil Sayyari, Yamin |
| dc.subject.proposal.eng.fl_str_mv |
Additive mapping F-hom-der Fixed point method Hyers-Ulam stability System of additive functional equations |
| topic |
Additive mapping F-hom-der Fixed point method Hyers-Ulam stability System of additive functional equations |
| description |
In this article, we solve the system of additive functional equations: fx y gx gy gx y f y x fx 2 , 2 4 ⎧ ⎨ ⎩ ( ) () () ( ) ( ) () +− = +− −= and prove the Hyers-Ulam stability of the system of additive functional equations in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of f -hom-ders in Banach algebras. |
| publishDate |
2023 |
| dc.date.accessioned.none.fl_str_mv |
2023-09-27T22:24:48Z |
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2023-09-27T22:24:48Z |
| dc.date.issued.none.fl_str_mv |
2023-02-13 |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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Text |
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info:eu-repo/semantics/article |
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http://purl.org/redcol/resource_type/ART |
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Paokanta, Siriluk, Dehghanian, Mehdi, Park, Choonkil and Sayyari, Yamin. "A system of additive functional equations in complex Banach algebras" Demonstratio Mathematica, vol. 56, no. 1, 2023, pp. 20220165. https://doi.org/10.1515/dema-2022-0165 |
| dc.identifier.issn.spa.fl_str_mv |
0219-8878 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/11323/10522 |
| dc.identifier.doi.none.fl_str_mv |
10.1515/dema-2022-0165 |
| dc.identifier.eissn.spa.fl_str_mv |
1793-6977 |
| dc.identifier.instname.spa.fl_str_mv |
Corporación Universidad de la Costa |
| dc.identifier.reponame.spa.fl_str_mv |
REDICUC - Repositorio CUC |
| dc.identifier.repourl.spa.fl_str_mv |
https://repositorio.cuc.edu.co/ |
| identifier_str_mv |
Paokanta, Siriluk, Dehghanian, Mehdi, Park, Choonkil and Sayyari, Yamin. "A system of additive functional equations in complex Banach algebras" Demonstratio Mathematica, vol. 56, no. 1, 2023, pp. 20220165. https://doi.org/10.1515/dema-2022-0165 0219-8878 10.1515/dema-2022-0165 1793-6977 Corporación Universidad de la Costa REDICUC - Repositorio CUC |
| url |
https://hdl.handle.net/11323/10522 https://repositorio.cuc.edu.co/ |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.relation.ispartofjournal.spa.fl_str_mv |
International Journal of Geometric Methods in Modern Physics |
| dc.relation.references.spa.fl_str_mv |
[1] M. Mirzavaziri and M. S. Moslehian, Automatic continuity of σ-derivations on ∗ C -algebras, Proc. Am. Math. Soc. 134 (2006), no. 11, 3319–3327. [2] C. Park, J. Lee, and X. Zhang, Additive s-functional inequality and hom-derivations in Banach algebras, J. Fixed Point Theory Appl. 21 (2019), Paper No. 18, DOI: https://doi.org/10.1007/s11784-018-0652-0. [3] M. Dehghanian, C. Park, and Y. Sayyari, On the stability of hom-der on Banach algebras (preprint). [4] A. Kheawborisuk, S. Paokanta, and J. Senasukh, Ulam stability of hom-ders in fuzzy Banach algebars, C. Park, AIMS Math. 7 (2022), no. 9, 16556–16568, DOI: https://doi.org/10.3934/math.2022907. [5] S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publications, New York, 1960. [6] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222–224. [7] M. Dehghanian and S. M. S. Modarres, Ternary γ-homomorphisms and ternary γ-derivations on ternary semigroups, J. Inequal. Appl. 2012 (2012), Paper No. 34, DOI: https://doi.org/10.1186/1029-242X-2012-34. [8] M. Dehghanian, S. M. S. Modarres, C. Park, and D. Shin, ∗ C -Ternary 3-derivations on ∗ C -ternary algebras, J. Inequal. Appl. 2013 (2013), Paper No. 124, DOI: https://doi.org/10.1186/1029-242X-2013-124. [9] M. Dehghanian and C. Park, ∗ C -Ternary 3-homomorphisms on ∗ C -ternary algebras, Results Math. 66 (2014), 385–404, DOI: https://doi.org/10.1007/s00025-014-0383-5. [10] M. Dehghanian, Y. Sayyari, and C. Park, Hadamard homomorphisms and Hadamard derivations on Banach algebras, Miskolc Math. Notes (in press). [11] C. Park, J. M. Rassias, A. Bodaghi, and S. Kim, Approximate homomorphisms from ternary semigroups to modular spaces, Rev. R. Acad. Cienc. Exactas Fiiis. Nat. Ser. A Mat. RACSAM 113 (2019), no. 3, 2175–2188, DOI: https://doi.org/10.1007/ s13398-018-0608-7. [12] C. Park, K. Tamilvanan, G. Balasubramanian, B. Noori, and A. Najati, On a functional equation that has the quadraticmultiplicative property, Open Math. 18 (2020), 837–845, DOI: https://doi.org/10.1515/math-2020-0032. [13] A. Thanyacharoen and W. Sintunavarat, The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimdean spaces, Demonstr. Math. 53 (2020), 174–192, DOI: https://doi.org/10.1515/dema2020-0009. [14] A. Thanyacharoen and W. Sintunavarat, On new stability results for composite functional equations in quasi-β-normed spaces, Demonstr. Math. 54 (2021), 68–84, DOI: https://doi.org/10.1515/dema-2021-0002. [15] Y. Sayyari, M. Dehghanian, C. Park, and J. Lee, Stability of hyper homomorphisms and hyper derivations in complex Banach algebras, AIMS Math. 7 (2022), no. 6, 10700–10710, DOI: https://doi.org/10.3934/math.2022597. [16] I. Hwang and C. Park, Bihom derivations in Banach algebras, J. Fixed Point Theory Appl. 21 (2019), no. 3, Paper No. 81, DOI: https://doi.org/10.1007/s11784-019-0722-x. [17] G. Lu and C. Park, Hyers-Ulam stability of general Jensen-type mappings in Banach algebras, Results Math. 66 (2014), 87–98, DOI: https://doi.org/10.1007/s00025-014-0365-7. [18] C. Park, An additive (α, β)-functional equation and linear mappings in Banach spaces, J. Fixed Point Theory Appl. 18 (2016), 495–504, DOI: https://doi.org/10.1007/s11784-016-0283-2. [19] C. Park, The stability of an additive (ρ ρ, ) 1 2 -functional inequality in Banach spaces, J. Math. Inequal. 13 (2019), 95–104, DOI: https://doi.org/10.7153/jmi-2019-13-07. [20] J. Brzdȩk, L. Cădariu, and K. Ciepliński, Fixed point theory and the Ulam stability, J. Funct. Spaces 2014 (2014), Article ID 829419, DOI: https://doi.org/10.1155/2014/829419. [21] J. Brzdȩk, E. Karapinar, and A. Petruşel, A fixed point theorem and the Ulam stability in generalized dq-metric spaces, J. Math. Anal. Appl. 467 (2018), no. 1, 501–520, DOI: https://doi.org/10.1016/j.jmaa.2018.07.022. [22] D. Popa, G. Pugna, and I. Rasa, On Ulam stability of the second order linear differential equation, Adv. Theory Nonlinear Anal. Appl. 2 (2018), no. 2, 106–112. [23] A. Salim, M. Benchohra, E. Karapinar, and J. E. Lazreg, Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations, Adv. Difference Equations 2020 (2020), Paper No. 601, DOI: https://doi.org/10.1186/ s13662-020-03063-4. [24] A. Lachouri and A. Ardjouni, The existence and Ulam-Hyers stability results for generalized Hilfer fractional integrodifferential equations with nonlocal integral boundary conditions, Adv. Theory Nonlinear Anal. Appl. 6 (2022), no. 1, 101–117. [25] H. Mohamed, Sequential fractional pantograph differential equations with nonlocal boundary conditions: Uniqueness and Ulam-Hyers-Rassias stability, Results Nonlinear Anal. 5 (2022), no. 1, 29–41, DOI: https://doi.org/10.53006/rna.928654. [26] R. Atmania, Existence and stability results for a nonlinear implicit fractional differential equation with a discrete delay, Adv. Theory Nonlinear Anal. Appl. 6 (2022), no. 2, 246–257. [27] E. Karapinar, H. D. Binh, N. H. Luc, and N. H. Can, On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems, Adv. Difference Equations 2021 (2021), Paper No. 70, DOI: https://doi.org/10.1186/s13662- 021-03232-z. [28] J. E. Lazreg, S. Abbas, M. Benchohra, and E. Karapinar, Impulsive Caputo-Fabrizio fractional differential equations in b-metric spaces, Open Math. 19 (2021), 363–372, DOI: https://doi.org/10.1515/math-2021-0040. [29] R. S. Adigüzel, U. Aksoy, E. Karapinar, and I. M. Erhan, On the solution of a boundary value problem associated with a fractional differential equation, Math. Methods Appl. Sci. (in press), DOI: https://doi.org/10.1002/mma.6652. [30] R. S. Adigüzel, U. Aksoy, E. Karapinar, and I. M. Erhan, Uniqueness of solution for higher-order nonlinear fractional differential equations with multi-point and integral boundary conditions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115 (2021), Paper No. 155, DOI: https://doi.org/10.1007/s13398-021-01095-3. [31] R. S. Adigüzel, U. Aksoy, E. Karapinar, and I. M. Erhan, On the solutions of fractional differential equations via Geraghty type hybrid contractions, Appl. Comput. Math. 20 (2021), 313–333. [32] H. Afshari and E. Karapinar, A solution of the fractional differential equations in the setting of b-metric space, Carpathian Math. Publ. 13 (2021), 764–774, DOI: https://doi.org/10.15330/cmp.13.3.764-774. [33] H. Afshari, H. Shojaat, and M. S. Moradi, Existence of the positive solutions for a tripled system of fractional differential equations via integral boundary conditions, Results Nonlinear Anal. 4 (2021), Article ID 186193, DOI: https://doi.org/10. 53006/rna.938851. [34] M. Asadi, B. Moeini, A. Mukheimer, and H. Aydi, Complex valued M-metric spaces and related fixed point results via complex C-class functions, J. Inequal. Spec. Funct. 10 (2019), no. 1, 101–110. [35] B. Moeini, M. Asadi, H. Aydi, and M. S. Noorani, ∗ C -Algebra-valued M-metric spaces and some related fixed point results, Ital. J. Pure Appl. Math. 41 (2019), 708–723. [36] J. B. Diaz and B. Margolis, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Am. Math. Soc. 74 (1968), 305–309. [37] D. Mihet and V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008), no. 1, 567–572, DOI: https://doi.org/10.1016/j.jmaa.2008.01.100. [38] C. Park, Homomorphisms between Poisson ∗ JC -algebras, Bull. Braz. Math. Soc. 36 (2005), 79–97, DOI: https://doi.org/10. 1007/s00574-005-0029-z. |
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Atribución 4.0 Internacional (CC BY 4.0)© 2023 the author(s), published by De Gruyterhttps://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Paokanta, Siriluk4a62e6db88b6dda593496497e125107f600Dehghanian, Mehdi8ed2eeb8796dc9177f00813953d2d97b600Park, Choonkil852a7a2ade0160c54d9c195cf0578542600Sayyari, Yamin91387f0cae558530466e095655dbb9af6002023-09-27T22:24:48Z2023-09-27T22:24:48Z2023-02-13Paokanta, Siriluk, Dehghanian, Mehdi, Park, Choonkil and Sayyari, Yamin. "A system of additive functional equations in complex Banach algebras" Demonstratio Mathematica, vol. 56, no. 1, 2023, pp. 20220165. https://doi.org/10.1515/dema-2022-01650219-8878https://hdl.handle.net/11323/1052210.1515/dema-2022-01651793-6977Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/In this article, we solve the system of additive functional equations: fx y gx gy gx y f y x fx 2 , 2 4 ⎧ ⎨ ⎩ ( ) () () ( ) ( ) () +− = +− −= and prove the Hyers-Ulam stability of the system of additive functional equations in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of f -hom-ders in Banach algebras.10 páginasapplication/pdfengWorld Scientific Publishing Co. Pte LtdSingaporehttps://www.degruyter.com/document/doi/10.1515/dema-2022-0165/htmlA system of additive functional equations in complex Banach algebrasArtículo de revistahttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85International Journal of Geometric Methods in Modern Physics[1] M. Mirzavaziri and M. S. Moslehian, Automatic continuity of σ-derivations on ∗ C -algebras, Proc. Am. Math. Soc. 134 (2006), no. 11, 3319–3327.[2] C. Park, J. Lee, and X. Zhang, Additive s-functional inequality and hom-derivations in Banach algebras, J. Fixed Point Theory Appl. 21 (2019), Paper No. 18, DOI: https://doi.org/10.1007/s11784-018-0652-0.[3] M. Dehghanian, C. Park, and Y. Sayyari, On the stability of hom-der on Banach algebras (preprint).[4] A. Kheawborisuk, S. Paokanta, and J. Senasukh, Ulam stability of hom-ders in fuzzy Banach algebars, C. Park, AIMS Math. 7 (2022), no. 9, 16556–16568, DOI: https://doi.org/10.3934/math.2022907.[5] S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publications, New York, 1960.[6] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222–224.[7] M. Dehghanian and S. M. S. Modarres, Ternary γ-homomorphisms and ternary γ-derivations on ternary semigroups, J. Inequal. Appl. 2012 (2012), Paper No. 34, DOI: https://doi.org/10.1186/1029-242X-2012-34.[8] M. Dehghanian, S. M. S. Modarres, C. Park, and D. Shin, ∗ C -Ternary 3-derivations on ∗ C -ternary algebras, J. Inequal. Appl. 2013 (2013), Paper No. 124, DOI: https://doi.org/10.1186/1029-242X-2013-124.[9] M. Dehghanian and C. Park, ∗ C -Ternary 3-homomorphisms on ∗ C -ternary algebras, Results Math. 66 (2014), 385–404, DOI: https://doi.org/10.1007/s00025-014-0383-5.[10] M. Dehghanian, Y. Sayyari, and C. Park, Hadamard homomorphisms and Hadamard derivations on Banach algebras, Miskolc Math. Notes (in press).[11] C. Park, J. M. Rassias, A. Bodaghi, and S. Kim, Approximate homomorphisms from ternary semigroups to modular spaces, Rev. R. Acad. Cienc. Exactas Fiiis. Nat. Ser. A Mat. RACSAM 113 (2019), no. 3, 2175–2188, DOI: https://doi.org/10.1007/ s13398-018-0608-7.[12] C. Park, K. Tamilvanan, G. Balasubramanian, B. Noori, and A. Najati, On a functional equation that has the quadraticmultiplicative property, Open Math. 18 (2020), 837–845, DOI: https://doi.org/10.1515/math-2020-0032.[13] A. Thanyacharoen and W. Sintunavarat, The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimdean spaces, Demonstr. Math. 53 (2020), 174–192, DOI: https://doi.org/10.1515/dema2020-0009.[14] A. Thanyacharoen and W. Sintunavarat, On new stability results for composite functional equations in quasi-β-normed spaces, Demonstr. Math. 54 (2021), 68–84, DOI: https://doi.org/10.1515/dema-2021-0002.[15] Y. Sayyari, M. Dehghanian, C. Park, and J. Lee, Stability of hyper homomorphisms and hyper derivations in complex Banach algebras, AIMS Math. 7 (2022), no. 6, 10700–10710, DOI: https://doi.org/10.3934/math.2022597.[16] I. Hwang and C. Park, Bihom derivations in Banach algebras, J. Fixed Point Theory Appl. 21 (2019), no. 3, Paper No. 81, DOI: https://doi.org/10.1007/s11784-019-0722-x.[17] G. Lu and C. Park, Hyers-Ulam stability of general Jensen-type mappings in Banach algebras, Results Math. 66 (2014), 87–98, DOI: https://doi.org/10.1007/s00025-014-0365-7.[18] C. Park, An additive (α, β)-functional equation and linear mappings in Banach spaces, J. Fixed Point Theory Appl. 18 (2016), 495–504, DOI: https://doi.org/10.1007/s11784-016-0283-2.[19] C. Park, The stability of an additive (ρ ρ, ) 1 2 -functional inequality in Banach spaces, J. Math. Inequal. 13 (2019), 95–104, DOI: https://doi.org/10.7153/jmi-2019-13-07.[20] J. Brzdȩk, L. Cădariu, and K. Ciepliński, Fixed point theory and the Ulam stability, J. Funct. Spaces 2014 (2014), Article ID 829419, DOI: https://doi.org/10.1155/2014/829419.[21] J. Brzdȩk, E. Karapinar, and A. Petruşel, A fixed point theorem and the Ulam stability in generalized dq-metric spaces, J. Math. Anal. Appl. 467 (2018), no. 1, 501–520, DOI: https://doi.org/10.1016/j.jmaa.2018.07.022.[22] D. Popa, G. Pugna, and I. Rasa, On Ulam stability of the second order linear differential equation, Adv. Theory Nonlinear Anal. Appl. 2 (2018), no. 2, 106–112.[23] A. Salim, M. Benchohra, E. Karapinar, and J. E. Lazreg, Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations, Adv. Difference Equations 2020 (2020), Paper No. 601, DOI: https://doi.org/10.1186/ s13662-020-03063-4.[24] A. Lachouri and A. Ardjouni, The existence and Ulam-Hyers stability results for generalized Hilfer fractional integrodifferential equations with nonlocal integral boundary conditions, Adv. Theory Nonlinear Anal. Appl. 6 (2022), no. 1, 101–117.[25] H. Mohamed, Sequential fractional pantograph differential equations with nonlocal boundary conditions: Uniqueness and Ulam-Hyers-Rassias stability, Results Nonlinear Anal. 5 (2022), no. 1, 29–41, DOI: https://doi.org/10.53006/rna.928654.[26] R. Atmania, Existence and stability results for a nonlinear implicit fractional differential equation with a discrete delay, Adv. Theory Nonlinear Anal. Appl. 6 (2022), no. 2, 246–257.[27] E. Karapinar, H. D. Binh, N. H. Luc, and N. H. Can, On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems, Adv. Difference Equations 2021 (2021), Paper No. 70, DOI: https://doi.org/10.1186/s13662- 021-03232-z.[28] J. E. Lazreg, S. Abbas, M. Benchohra, and E. 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corporada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.
 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