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Strong F-convexity and concavity and refinements of some classical inequalities
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Strong F-convexity and concavity and refinements of some classical inequalities
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Journal Article
Strong F-convexity and concavity and refinements of some classical inequalities
2024
Overview
The concept of strong
F
-convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show that in more effective and specific analysis this concept is very useful, and especially its generalization, namely strong
F
-concavity. Using this concept, refinements of the Young inequality are given as a model case. A general form of the self-improving property for Jensen type inequalities is presented. We show that a careful choice of control functions for convex or concave functions can give a control over these refinements and produce refinements of the power mean inequalities.
Publisher
Springer International Publishing,Springer Nature B.V
