THE HERMITE-HADAMARD TYPE INEQUALITIES FOR OPERATOR p-CONVEX FUNCTIONS IN HILBERT SPACE (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.

Abstract Convexity and Hermite-Hadamard Type Inequalities

Journal of Inequalities and Applications, 2009

The deriving Hermite-Hadamard type inequalities for certain classes of abstract convex functions are considered totally, the inequalities derived for some of these classes before are summarized, new inequalities for others are obtained, and for one class of these functions the results on R 2 are generalized to R n. By considering a concrete area in R n , the derived inequalities are illustrated.

On the generalized inequalities of the Hermite-Hadamard type

Filomat, 2021

In this paper, we establish new Hermite-Hadamard inequalities for h-convex functions, with in the framework of a previously defined generalized integral. The results obtained, generalize or complete, several reported in the literature. Some final remarks show the strength and scope of our results.

Some New Hermite-Hadamard Type Inequalities for Convex Functions

2020

Convex sets and convex functions play a fundamental role in the development of various fields of pure and applied mathematics. Recently, many new generalizations of inequalities with respect to Hermite-Hadamard have been proposed in the literature. In this paper, some new inequalities of the Hermite-Hadamard type for differentiable convex functions are given. These new inequalities are based on the second derivative functions.

Some Results on Hermite-Hadamard Type Inequality through Convexity

Turkish Journal of Analysis and Number Theory, 2014

Our aim in this article to establish various inequalities for some differentiable mapping that are connected with illustrious Hermite-Hadamard integral inequality for mapping whose absolute values of derivatives are convex. The new integral inequalities are then applied to some special means and as well as numerical integration to obtain some better estimates.