The logarithmic mean of two convex functionals
Mustapha Ra\"issouli, Shigeru Furuichi
TL;DR
This paper introduces a new logarithmic mean for convex functionals, extending the concept from positive operators, and discusses related inequalities with direct operator-theoretic implications.
Contribution
It defines a novel logarithmic mean for convex functionals and derives inequalities, extending operator mean concepts without relying on operator theory.
Findings
Defined the logarithmic mean for convex functionals
Established inequalities involving this new mean
Extended operator mean concepts to convex functionals
Abstract
The purpose of this paper is to introduce the logarithmic mean of two convex functionals that extends the logarithmic mean of two positive operators. Some inequalities involving this functional mean are discussed as well. The operator versions of the functional theoretical results obtained here are immediately deduced without referring to the theory of operator means.
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Taxonomy
TopicsMathematical Inequalities and Applications · Functional Equations Stability Results · Analytic and geometric function theory