Abstract
In this paper, we introduce operator (p, h)‐convex functions and establish a Hermite–Hadamard inequality for these functions. As application, we obtain several trace and singular value inequalities of operators.
Highlights
In recent years, several extensions and generalizations have been considered for classical convexity and the theory of inequalities has made essential contributions to many areas of mathematics.In 1973, Elliott Lieb published a ground-breaking article on operator inequalities [1]. is and a subsequent article by Lieb and Ruskai [2] have had a profound effect on quantum statistical mechanics and more recently on quantum information theory
Two elegant examples are those of Nielsen and Petz [3] and Ruskai [4], which use the analytic representations for operator convex functions
Motivated by the above results, we investigate in this paper the operator version of the Hermite–Hadamard inequality for operator (α, h)-preinvex function
Summary
Several extensions and generalizations have been considered for classical convexity and the theory of inequalities has made essential contributions to many areas of mathematics.In 1973, Elliott Lieb published a ground-breaking article on operator inequalities [1]. is and a subsequent article by Lieb and Ruskai [2] have had a profound effect on quantum statistical mechanics and more recently on quantum information theory. He proved that if f: I ⊆ [0, ∞) ⟶ R is an operator s-convex function, the following inequalities hold: 2s− Journal of Mathematics e following inequalities due to the authors [14] give the Hermite–Hadamard inequalities for operator h-convex function.
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