AIMS Mathematics (Jun 2020)
Refinements of Jensen’s and McShane’s inequalities with applications
Abstract
In this article, we consider the generalized forms of the Jensen’s inequality given by Jessen and McShane for isotonic linear functionals, derive several refinements for the Jessen’s and McShane’s inequalities connected to certain functions from the linear space, generalize the Jessen’s and McShane’s inequalities pertaining n certain functions. As applications, we provide some improvements for the generalized means, Holder and generalized Beck’s inequalities.
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