On Some Hadamard Type Inequalities for MT- Convex Functions

Abstract

In this paper, we establish some new Hadamard type inequalities for MTconvex functions and give few applications for some special means.

Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals

“…In [30] (see also [27,29]), Tunc and Yidirim defined the following so-called MT-convex function: Definition 1.3. A function: I ⊆ R → R is said to belong to the class of MT(I), if it is nonnegative and for all x, y ∈ I and t ∈ (0, 1) satisfies the following inequality: For other recent results concerning Hermite-Hadamard type inequalities through various classes of convex functions, see [1,3,5,7,8,9,12,10,17,20,22,24,25,28] and the references cited therein.…”

Generalizations of Hermite--Hadamard type inequalities for MT-convex functions

“…In [29] (see also [26][27][28]), Tunç and Yidirim defined the so-called MT-convex function as follows. A nonnegative function φ : I → R is said to be MT-convex on the interval I if the inequality…”

“…In the above propositions we have used the fact that every positive convex function is a MT-convex function [28].…”

New Hermite-Hadamard inequalities for twice differentiable ϕ -MT-preinvex functions

“…In [29] (see also [28]), Tunç and Yidirim defined the notion of MT-convex as follows. Definition 1.6.…”

“…For some interesting and significant integral inequalities concerning with the MT-convex functions, one can see in the recent papers [14,21,[27][28][29]. It can be easily observed that convexity means just Jensen-convex when t = In [18],Özdemir et al established inequalities for twice differentiable m-convex functions which are connected with Hermite-Hadamard inequality, and they used the following lemma to prove their results.…”