Characterizations of upper and lower (α, β, θ, δ, I)-continuous multifunctions
Given a multifunction F : (X; _ ) ! (Y; _), _; _ oper-ators on (X; _ ), _; _ operators on (Y; _) and I a proper ideal on X. The purpose of the present paper is to introduce, study and characterize upper and lower (_; _; _; _; I)-continuous multifunctions, its relation with another class of continuou...
- Autores:
-
ROSAS, ENNIS
Carpintero, Carlos
Sanabria, Jose
Vielma, J.
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2021
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/8461
- Acceso en línea:
- https://hdl.handle.net/11323/8461
https://repositorio.cuc.edu.co/
- Palabra clave:
- Continuous multifunctions
Multifunction
Continuous upper and lower multifunction
- Rights
- openAccess
- License
- CC0 1.0 Universal
| id |
RCUC2_4ca1864455ac9b149c488ca4f040d3f6 |
|---|---|
| oai_identifier_str |
oai:repositorio.cuc.edu.co:11323/8461 |
| network_acronym_str |
RCUC2 |
| network_name_str |
REDICUC - Repositorio CUC |
| repository_id_str |
|
| dc.title.eng.fl_str_mv |
Characterizations of upper and lower (α, β, θ, δ, I)-continuous multifunctions |
| title |
Characterizations of upper and lower (α, β, θ, δ, I)-continuous multifunctions |
| spellingShingle |
Characterizations of upper and lower (α, β, θ, δ, I)-continuous multifunctions Continuous multifunctions Multifunction Continuous upper and lower multifunction |
| title_short |
Characterizations of upper and lower (α, β, θ, δ, I)-continuous multifunctions |
| title_full |
Characterizations of upper and lower (α, β, θ, δ, I)-continuous multifunctions |
| title_fullStr |
Characterizations of upper and lower (α, β, θ, δ, I)-continuous multifunctions |
| title_full_unstemmed |
Characterizations of upper and lower (α, β, θ, δ, I)-continuous multifunctions |
| title_sort |
Characterizations of upper and lower (α, β, θ, δ, I)-continuous multifunctions |
| dc.creator.fl_str_mv |
ROSAS, ENNIS Carpintero, Carlos Sanabria, Jose Vielma, J. |
| dc.contributor.author.spa.fl_str_mv |
ROSAS, ENNIS Carpintero, Carlos Sanabria, Jose Vielma, J. |
| dc.subject.eng.fl_str_mv |
Continuous multifunctions Multifunction Continuous upper and lower multifunction |
| topic |
Continuous multifunctions Multifunction Continuous upper and lower multifunction |
| description |
Given a multifunction F : (X; _ ) ! (Y; _), _; _ oper-ators on (X; _ ), _; _ operators on (Y; _) and I a proper ideal on X. The purpose of the present paper is to introduce, study and characterize upper and lower (_; _; _; _; I)-continuous multifunctions, its relation with another class of continuous multifunctions. Also, we introduce a general decomposition form for this class of continuous multifunction. |
| publishDate |
2021 |
| dc.date.accessioned.none.fl_str_mv |
2021-07-12T13:30:13Z |
| dc.date.available.none.fl_str_mv |
2021-07-12T13:30:13Z |
| dc.date.issued.none.fl_str_mv |
2021 |
| dc.type.spa.fl_str_mv |
Artículo de revista |
| dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 |
| dc.type.content.spa.fl_str_mv |
Text |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/ART |
| dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
| format |
http://purl.org/coar/resource_type/c_6501 |
| status_str |
acceptedVersion |
| dc.identifier.issn.spa.fl_str_mv |
1027-4634 2411-0620 |
| dc.identifier.uri.spa.fl_str_mv |
https://hdl.handle.net/11323/8461 |
| dc.identifier.doi.spa.fl_str_mv |
doi:10.30970/ms.55.2.206-213 |
| 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 |
1027-4634 2411-0620 doi:10.30970/ms.55.2.206-213 Corporación Universidad de la Costa REDICUC - Repositorio CUC |
| url |
https://hdl.handle.net/11323/8461 https://repositorio.cuc.edu.co/ |
| dc.language.iso.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.references.spa.fl_str_mv |
1. M. Akdag, On upper and lower I-continuos multifunctions, Far East J. Math. Sci., 25 (2007), №1, 49–57. 2. A. Al-Omari, M.S.M. Noorani, Contra-I-continuous and almost I-continuous functions, Int. J. Math. Math. Sci., 9 (2007), 169–179. 3. C. Arivazhagi, N. Rajesh, On upper and lower weakly I-continuous multifunctions, Ital. J. Pure Appl. Math., 36 (2016), 899–912. 4. C. Arivazhagi, N. Rajesh, On upper and lower I-nontinuous multifunctions, Bol. Soc. Paran. Mat., 36 (2018), №2, 99–106. 5. C. Arivazhagi, N. Rajesh, Nearly I-continuous multifunctions, Bol. Soc. Paran. Mat., 37 (2019), №11, 33–38. 6. C. Arivazhagi, N. Rajesh, S. Shanthi, On upper and lower almost contra-I-continuous multifunctions, Int. J. Pure Appl. Math., 115 (2017), №4, 787–799. 7. C. Arivazhagi, N. Rajesh, On upper and lower almost I-continuous multifunctions, submitted. 8. C. Arivazhagi, N. Rajesh, On slightly I-continuous multifunctions, Journal of New Results in Science, 11 (2016), 17–23. 9. D. Carnahan, Locally nearly compact spaces, Boll. Un. mat. Ital., 4 (1972), №6, 143–153. 10. C. Carpintero, J. Pacheco, N. Rajesh, E. Rosas, S. Saranyasri, Properties of nearly ω-continuous multifunctions, Acta Univ. Sapientiae Math., 9 (2017), №1, 13–25. 11. C. Carpintero, E. Rosas, J. Moreno, More on upper and lower almost nearly I-continuous multifunctions, Int. J. Pure Appl. Math., 117 (2017), №3, 521–537. 12. C. Carpintero, N. Rajesn, E. Rosas, S. Saranyasri, On upper and lower contra ω-continuous multifunctions, Novi Sad J. Math., 44 (2014), №1, 143–151. 13. C. Carpintero, N. Rajesn, E. Rosas, S. Saranyasri, On upper and lower faintly ω-continuous multifunctions, Bol. Mat., 21 (2014), №1, 1–8. 14. E. Ekici, Nearly continuous multifunctions, Acta Math. Univ. Comenianae, 72 (2003), 229–235. 15. E. Ekici, Almost nearly continuous multifunctions, Acta Math. Univ. Comenianae, 73 (2004), 175–186. 16. E. Ekici, S. Jafari, V. Popa, On Almost contra-continuous multifunctions, Lobachevskii J. Math., 30 (2009), №2, 124–131. 17. E. Ekici, S. Jafari, T. Noiri, On upper and lower contra-continuous multifunctions, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), Tomul LIV, 2008, 75–85. 18. D.S. Jankovic, T.R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97 (1990), №4, 295–310. 19. N. Levine, Semi open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36–41. 20. A. Kambir, I. J. Reilly, On almost l-continuous multifunctions, Hacet. J. Math. Stat., 35 (2005), №2, 181–188. 21. S. Kasahara, Operation compact spaces, Math. Japonica, 24 (1966), 97–105. 22. J. K. Kolii, C.P. Arya, Strongly and perfectly continuous multifunctions, Sci. Stud. Res. Ser. Math. Inform., 20 (2010), №1, 103–118. 23. J.K. Kohli, C.P. Arya, Upper and lower (almost) completely continuous multifunctions, preprint. 24. K. Kuratowski, Topology, Academic Press, New York, 1966. 25. A.S. Mashhour, M.E. Abd El-Monsef, El-Deep on precontinuous and weak precontinuous mappings, Proced. Phys. Soc. Egypt, 53 (1982), 47–53. 26. T. Noiri, V. Popa, On upper and lower M-continuos multifunctions, Filomat, 14 (2000), 73–86. 27. T. Noiri, V. Popa, Slightly m-continuos multifunctions, Bulletin of the Institute of Mathematics Academia Sinica (New Series), 1 (2006), №4, 485–505. 28. T. Noiri, V. Popa, Almost weakly continuos multifunctions, Demonstrat. Math., 22 (1993), №2, 362–380. 29. V. Popa, Some properties of H-almost continuous multifunctions, Chaos Solitons Fractals, 12 (2000), 2387–2394. 30. E. Rosas, C. Carpintero, J. Moreno, Upper and lower (I, J) continuous multifunctions, Int. J. Pure Appl. Math., 117 (2017), №1, 87–97. 31. E. Rosas, C. Carpintero, J. Sanabria, Weakly (I, J) continuous multifunctions and contra (I, J) continuous multifunctions, Ital. J. Pure Appl. Math., 41 (2019), 547–556. 32. E. Rosas, C. Carpintero, J. Moreno, Upper and lower (I,J)-continuous multifunctions, Int. J. Pure Appl. Math., 117 (2017), №1. 33. E. Rosas, C. Carpintero, J. Sanabria, Almost contra (I, J)-continuous multifunctions, Novi Sad J. Math. on line March 28, 2019. 34. R.E. Simithson, Almost and weak continuity for multifunctions, Bull. Calcutta Math. Soc., 70 (1978), 383–390. 35. M. Stone, Applications of the theory of boolean rings to general topology, Trans. Amer. Math. Soc., 41 (1937), 374–381. 36. J. Vielma, E. Rosas, (α, β, θ, δ, I)-continuous mappings and their decomposition, Divulgaciones Matematicas, 12 (2004), №1, 53–64. 37. I. Zorlutuna, I-continuous multifunctions, Filomat, 27 (2013), №1, 155–162. |
| dc.rights.spa.fl_str_mv |
CC0 1.0 Universal |
| dc.rights.uri.spa.fl_str_mv |
http://creativecommons.org/publicdomain/zero/1.0/ |
| dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
| dc.rights.coar.spa.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| rights_invalid_str_mv |
CC0 1.0 Universal http://creativecommons.org/publicdomain/zero/1.0/ http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.mimetype.spa.fl_str_mv |
application/pdf |
| dc.publisher.spa.fl_str_mv |
Corporación Universidad de la Costa |
| dc.source.spa.fl_str_mv |
Matematychni Studii |
| institution |
Corporación Universidad de la Costa |
| bitstream.url.fl_str_mv |
https://repositorio.cuc.edu.co/bitstreams/cff13744-5922-4b27-b3b1-e83802087134/download https://repositorio.cuc.edu.co/bitstreams/fded15e7-9b50-4423-be4b-97a891df1505/download https://repositorio.cuc.edu.co/bitstreams/84435931-368d-47d3-a8d6-e549ed508e33/download https://repositorio.cuc.edu.co/bitstreams/c5b03ee8-6096-4576-bb52-4996453ad657/download https://repositorio.cuc.edu.co/bitstreams/fc8af069-23c5-40b0-a9ea-6bc542e12aff/download |
| bitstream.checksum.fl_str_mv |
c3f056bc412cadbc3f56b4175a250969 42fd4ad1e89814f5e4a476b409eb708c e30e9215131d99561d40d6b0abbe9bad 6c3b3bc9dd06633844a4cd3af0effc3c b10a48bb3477787afeab86a7337a9c6b |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio de la Universidad de la Costa CUC |
| repository.mail.fl_str_mv |
repdigital@cuc.edu.co |
| _version_ |
1811760763104133120 |
| spelling |
ROSAS, ENNISCarpintero, CarlosSanabria, JoseVielma, J.2021-07-12T13:30:13Z2021-07-12T13:30:13Z20211027-46342411-0620https://hdl.handle.net/11323/8461doi:10.30970/ms.55.2.206-213Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/Given a multifunction F : (X; _ ) ! (Y; _), _; _ oper-ators on (X; _ ), _; _ operators on (Y; _) and I a proper ideal on X. The purpose of the present paper is to introduce, study and characterize upper and lower (_; _; _; _; I)-continuous multifunctions, its relation with another class of continuous multifunctions. Also, we introduce a general decomposition form for this class of continuous multifunction.ROSAS, ENNIS-will be generated-orcid-0000-0001-8123-9344-600Carpintero, Carlos-will be generated-orcid-0000-0003-3831-952X-600Sanabria, Jose-will be generated-orcid-0000-0003-1025-1834-600Vielma, J.application/pdfengCorporación Universidad de la CostaCC0 1.0 Universalhttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Matematychni StudiiContinuous multifunctionsMultifunctionContinuous upper and lower multifunctionCharacterizations of upper and lower (α, β, θ, δ, I)-continuous multifunctionsArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersion1. M. Akdag, On upper and lower I-continuos multifunctions, Far East J. Math. Sci., 25 (2007), №1, 49–57.2. A. Al-Omari, M.S.M. Noorani, Contra-I-continuous and almost I-continuous functions, Int. J. Math. Math. Sci., 9 (2007), 169–179.3. C. Arivazhagi, N. Rajesh, On upper and lower weakly I-continuous multifunctions, Ital. J. Pure Appl. Math., 36 (2016), 899–912.4. C. Arivazhagi, N. Rajesh, On upper and lower I-nontinuous multifunctions, Bol. Soc. Paran. Mat., 36 (2018), №2, 99–106.5. C. Arivazhagi, N. Rajesh, Nearly I-continuous multifunctions, Bol. Soc. Paran. Mat., 37 (2019), №11, 33–38.6. C. Arivazhagi, N. Rajesh, S. Shanthi, On upper and lower almost contra-I-continuous multifunctions, Int. J. Pure Appl. Math., 115 (2017), №4, 787–799.7. C. Arivazhagi, N. Rajesh, On upper and lower almost I-continuous multifunctions, submitted.8. C. Arivazhagi, N. Rajesh, On slightly I-continuous multifunctions, Journal of New Results in Science, 11 (2016), 17–23.9. D. Carnahan, Locally nearly compact spaces, Boll. Un. mat. Ital., 4 (1972), №6, 143–153.10. C. Carpintero, J. Pacheco, N. Rajesh, E. Rosas, S. Saranyasri, Properties of nearly ω-continuous multifunctions, Acta Univ. Sapientiae Math., 9 (2017), №1, 13–25.11. C. Carpintero, E. Rosas, J. Moreno, More on upper and lower almost nearly I-continuous multifunctions, Int. J. Pure Appl. Math., 117 (2017), №3, 521–537.12. C. Carpintero, N. Rajesn, E. Rosas, S. Saranyasri, On upper and lower contra ω-continuous multifunctions, Novi Sad J. Math., 44 (2014), №1, 143–151.13. C. Carpintero, N. Rajesn, E. Rosas, S. Saranyasri, On upper and lower faintly ω-continuous multifunctions, Bol. Mat., 21 (2014), №1, 1–8.14. E. Ekici, Nearly continuous multifunctions, Acta Math. Univ. Comenianae, 72 (2003), 229–235.15. E. Ekici, Almost nearly continuous multifunctions, Acta Math. Univ. Comenianae, 73 (2004), 175–186.16. E. Ekici, S. Jafari, V. Popa, On Almost contra-continuous multifunctions, Lobachevskii J. Math., 30 (2009), №2, 124–131.17. E. Ekici, S. Jafari, T. Noiri, On upper and lower contra-continuous multifunctions, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), Tomul LIV, 2008, 75–85.18. D.S. Jankovic, T.R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97 (1990), №4, 295–310.19. N. Levine, Semi open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36–41.20. A. Kambir, I. J. Reilly, On almost l-continuous multifunctions, Hacet. J. Math. Stat., 35 (2005), №2, 181–188.21. S. Kasahara, Operation compact spaces, Math. Japonica, 24 (1966), 97–105.22. J. K. Kolii, C.P. Arya, Strongly and perfectly continuous multifunctions, Sci. Stud. Res. Ser. Math. Inform., 20 (2010), №1, 103–118.23. J.K. Kohli, C.P. Arya, Upper and lower (almost) completely continuous multifunctions, preprint.24. K. Kuratowski, Topology, Academic Press, New York, 1966.25. A.S. Mashhour, M.E. Abd El-Monsef, El-Deep on precontinuous and weak precontinuous mappings, Proced. Phys. Soc. Egypt, 53 (1982), 47–53.26. T. Noiri, V. Popa, On upper and lower M-continuos multifunctions, Filomat, 14 (2000), 73–86.27. T. Noiri, V. Popa, Slightly m-continuos multifunctions, Bulletin of the Institute of Mathematics Academia Sinica (New Series), 1 (2006), №4, 485–505.28. T. Noiri, V. Popa, Almost weakly continuos multifunctions, Demonstrat. Math., 22 (1993), №2, 362–380.29. V. Popa, Some properties of H-almost continuous multifunctions, Chaos Solitons Fractals, 12 (2000), 2387–2394.30. E. Rosas, C. Carpintero, J. Moreno, Upper and lower (I, J) continuous multifunctions, Int. J. Pure Appl. Math., 117 (2017), №1, 87–97.31. E. Rosas, C. Carpintero, J. Sanabria, Weakly (I, J) continuous multifunctions and contra (I, J) continuous multifunctions, Ital. J. Pure Appl. Math., 41 (2019), 547–556.32. E. Rosas, C. Carpintero, J. Moreno, Upper and lower (I,J)-continuous multifunctions, Int. J. Pure Appl. Math., 117 (2017), №1.33. E. Rosas, C. Carpintero, J. Sanabria, Almost contra (I, J)-continuous multifunctions, Novi Sad J. Math. on line March 28, 2019.34. R.E. Simithson, Almost and weak continuity for multifunctions, Bull. Calcutta Math. Soc., 70 (1978), 383–390.35. M. Stone, Applications of the theory of boolean rings to general topology, Trans. Amer. Math. Soc., 41 (1937), 374–381.36. J. Vielma, E. Rosas, (α, β, θ, δ, I)-continuous mappings and their decomposition, Divulgaciones Matematicas, 12 (2004), №1, 53–64.37. I. Zorlutuna, I-continuous multifunctions, Filomat, 27 (2013), №1, 155–162.PublicationORIGINALCHARACTERIZATIONS OF UPPER AND LOWER.pdfCHARACTERIZATIONS OF UPPER AND LOWER.pdfapplication/pdf307769https://repositorio.cuc.edu.co/bitstreams/cff13744-5922-4b27-b3b1-e83802087134/downloadc3f056bc412cadbc3f56b4175a250969MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.cuc.edu.co/bitstreams/fded15e7-9b50-4423-be4b-97a891df1505/download42fd4ad1e89814f5e4a476b409eb708cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83196https://repositorio.cuc.edu.co/bitstreams/84435931-368d-47d3-a8d6-e549ed508e33/downloade30e9215131d99561d40d6b0abbe9badMD53THUMBNAILCHARACTERIZATIONS OF UPPER AND LOWER.pdf.jpgCHARACTERIZATIONS OF UPPER AND LOWER.pdf.jpgimage/jpeg62423https://repositorio.cuc.edu.co/bitstreams/c5b03ee8-6096-4576-bb52-4996453ad657/download6c3b3bc9dd06633844a4cd3af0effc3cMD54TEXTCHARACTERIZATIONS OF UPPER AND LOWER.pdf.txtCHARACTERIZATIONS OF UPPER AND LOWER.pdf.txttext/plain26807https://repositorio.cuc.edu.co/bitstreams/fc8af069-23c5-40b0-a9ea-6bc542e12aff/downloadb10a48bb3477787afeab86a7337a9c6bMD5511323/8461oai:repositorio.cuc.edu.co:11323/84612024-09-17 11:02:27.011http://creativecommons.org/publicdomain/zero/1.0/CC0 1.0 Universalopen.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.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 |