Convex functions and the hadamard inequality
The Hadamard inequality is proven without resorting to any properties of the derivative. Only the convexity of the function in a closed interval is needed. Furthermore, if the existence of the integral is assumed, then the convexity requirement is weakened to convexity in the sense of Jensen. Both t...
- Autores:
-
Azpeitia, Alfonso G.
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1994
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/43486
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/43486
http://bdigital.unal.edu.co/33584/
- Palabra clave:
- Convex and concave functions
arithmetic means
convexity inequalities
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | The Hadamard inequality is proven without resorting to any properties of the derivative. Only the convexity of the function in a closed interval is needed. Furthermore, if the existence of the integral is assumed, then the convexity requirement is weakened to convexity in the sense of Jensen. Both the Hadamard inequality and a corresponding upper bound are generalized for integrals of the Stieljes type. |
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