Improvements of Jensen-Type Inequalities for Diamond-α Integrals

We give further improvements of the Jensen inequality and its converse on time scales, allowing also negative weights. These results generalize the Jensen inequality and its converse for both discrete and continuous cases. Further, we investigate the exponential and logarithmic convexity of the diff...

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Detalles Bibliográficos
Autores principales: Bibi, Rabia, Pečarić, Josip, Lipanović, Mirna Rodić
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897212/
https://www.ncbi.nlm.nih.gov/pubmed/27379320
http://dx.doi.org/10.1155/2014/580605
Descripción
Sumario:We give further improvements of the Jensen inequality and its converse on time scales, allowing also negative weights. These results generalize the Jensen inequality and its converse for both discrete and continuous cases. Further, we investigate the exponential and logarithmic convexity of the differences between the left-hand side and the right-hand side of these inequalities and present several families of functions for which these results can be applied.

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