Some Generalizations of Jensen's Inequality
Slavko Simic
TL;DR
This paper presents new generalizations and improvements of Jensen's and Jensen-Mercer inequalities for twice differentiable functions, removing the need for initial convexity assumptions, with applications in means and probability.
Contribution
It introduces generalized inequalities that extend Jensen's and Jensen-Mercer inequalities without assuming convexity, applicable to a broader class of functions.
Findings
Refined inequalities for twice differentiable functions.
Applications in Theory of Means and Probability.
No initial convexity assumption required.
Abstract
In this article we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where convexity property of the target function is not assumed in advance. They represents a refinement of these inequalities in the case of convex/concave functions with numerous applications in Theory of Means and Probability and Statistics.
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