Mathematical inequalities on some weighted means
Shigeru Furuichi, Kenjiro Yanagi, Hamid Reza Moradi
TL;DR
This paper investigates inequalities among weighted means, including logarithmic and Jensen's inequality gaps, providing new inequalities and operator inequalities to deepen understanding of mean relationships.
Contribution
It introduces novel inequalities involving weighted means, explores the Jensen's inequality gap via convex functions, and presents new operator inequalities.
Findings
New inequalities on weighted logarithmic means
Analysis of Jensen's inequality gap for convex functions
Introduction of operator inequalities related to means
Abstract
Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial inequalities on means are given. Some operator inequalities are also shown.
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Taxonomy
TopicsMathematical Inequalities and Applications · Functional Equations Stability Results · Mathematics and Applications