In this paper, we introduce operator s-convex functions and establish some Hermite-Hadamard type inequalities in which some operator s-convex functions of positive operators in Hilbert spaces are involved.

In the paper, the authors introduce a new notion "[Formula: see text]-convex function on the co-ordinates" and establish some Hermite-Hadamard type integral inequalities for [Formula: see text]-convex functions on the co-ordinates.

In this paper, we prove Hermite-Hadamard type inequalities for r-preinvex functions via fractional integrals. The results presented here would provide extensions of those given in earlier works.

Intensive studies aiming to extend the Hermite-Hadamard inequalities and explore some properties applications of these have been recently carried out. The contribution this paper falls within framework. We investigate refinements reverses for Hermite- Hadamard when integrand map is pointwise convex in its functional arguments. Our theoretical results obtained here immediately imply those operat...

Abstract In this paper, our aim is to consider the new class of log-convex fuzzy-interval-valued function known as log- s -convex functions (log- fuzzy-IVFs). By concept, we have introduced Hermite–Hadamard inequalities (HH-inequalities) by means fuzzy order relation. This relation defined level-wise through Kulisch–Miranker on interval space. Moreover, some Hermite–Hadamard–Fejér (HH–Fejér-ine...

Abstract In this study, we use the fuzzy order relation to show some novel variants of Hermite–Hadamard inequalities for pre-invex fuzzy-interval-valued mappings ( F-I∙V-Ms ), which term fuzzy-interval and Hermite–Hadamard–Fejér inequalities. This is defined as level space by Kulisch–Miranker relation. There are also new exceptional instances mentioned. The theory proposed in research shown wit...

In this paper, we introduce and study a new class of generalized functions, called generalized geometrically convex functions. We establish several basic inequalities related to generalized geometrically convex functions. We also derive several new inequalities of the Hermite-Hadamard type for generalized geometrically convex functions. Several special cases are discussed, which can be deduced ...

In this paper, we prove some Hermite-Hadamard type inequalities for operator geometrically convex functions non-commutative operators.

In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real numbers and give the error estimations for the trapezoidal formula.

It is well known that the Hermite–Hadamard inequality (called HH inequality) refines definition of convexity function f(x) defined on [a,b] by using integral from a to b. There are many generalizations or refinements inequality. Furthermore has applications several fields mathematics, including numerical analysis, functional and operator Recently, we gave types refined inequalities obtained whi...