A New Class of Operator Monotone Functions via Operator Means
arXiv:1603.08467 · doi:10.1080/03081087.2016.1160999
Abstract
In this paper, we obtain a new class of functions, which is developed via the Hermite--Hadamard inequality for convex functions. The well-known one-one correspondence between the class of operator monotone functions and operator connections declares that the obtained class represents the weighted logarithmic means. We shall also consider weighted identric mean and some relationships between various operator means. Among many things, we extended the weighted arithmetic--geometric operator mean inequality as and involving the considered operator means.
13 pages, to appear in Linear Multilinear Algebra (LAMA)