Some New Generalized Jensen and Hermite-Hadamard Inequalities for Operator h−Convex Functions (original) (raw)

Operator (h,m)-Convexity and Hermite-Hadamard Type Inequalities

Istanbul University - DergiPark, 2017

In this paper, firstly we define a new class of operator convex functions in Hilbert space, as operator (h,m)-convex functions. Later we give some properties of this class. Finally, we obtain some new inequalities via Hermite-Hadamard inequality for operator (h,m)-convex function.

On hermite-hadamard inequalities for h-preinvex functions

Filomat, 2014

The objective of this paper is to obtain some Hermite-Hadamard type inequalities for h-preinvex functions. Firstly, a new kind of generalized h-convex functions, termed h-preinvex functions, is introduced through relaxing the concept of h-convexity introduced by Varosanec. Some Hermite-Hadamard type inequalities for h-preinvex functions are established under certain conditions. Our results can be viewed as generalization of several previously known results. Results proved in this paper may stimulate further research in different areas of pure and applied sciences.

Some Hermite–Hadamard type inequalities for log-h-convex functions

Analysis, 2013

In this paper, we consider the class of modified h-convex functions, which was introduced by Toader [14]. We derive Hermite-Hadamard type inequalities for the modified h-convex functions. Some special cases are also discussed. We try to show that this class enjoys some nice properties which the convex functions have.

Properties of GA-h-Convex Functions in Connection to the Hermite–Hadamard–Fejér-Type Inequalities

Mathematics

In this study, the Hermite–Hadamard–Fejér inequalities for GA-h-convex are proved, and the results for particular classes of functions are highlighted. In addition, several generalizations of the Hermite–Hadamard inequalities are presented. Some features of functions H and F that are naturally linked to the Hermite–Hadamard–Fejér-type inequalities for GA-h-convex have also been discussed. Finally, we obtain applications of the results related to the p-logarithmic mean and the mean of order p.