The logarithmic mean of two 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.

Keywords

• functional means
• logarithmic mean of convex functionals
• functional inequalities
• 46n10
• 46a20
• 47a63
• 47n10