In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type via new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, identity for differentiable convex functions of first order is proved. Then, taking into account as an auxiliary result assistance Hölder, power-mean, Young, Jensen inequality, some estimations...

The superadditivity and monotonicity properties of some functionals associated with convex functions and the Hermite-Hadamard inequality in the general setting of linear spaces are investigated. Applications for norms and convex functions of a real variable are given. Some inequalities for arithmetic, geometric, harmonic, logarithmic and identric means are improved. 1. Introduction For any conv...

In this paper, we present a weighted version of the Hermite–Hadamard inequality for convex functions on time scales, with weights that are allowed to take some negative values, these are the Steffensen–Popoviciu and the Hermite–Hadamard weights. We also present some applications of this inequality.

In this work, we address and explore the concept of generalized \(m\)-preinvex functions on fractal sets along with linked local fractional integral inequalities. Additionally, some engrossing algebraic properties are presented to facilitate current initiated idea. Furthermore, prove latest variant Hermite-Hadamard type inequality employing proposed definition preinvexity. We also derive severa...

The following is the classical Hermite-Hadamard inequality [4, 5]: f ( a+ b 2 ) ≤ 1 b− a (S) ∫ b a f(x)dμ ≤ f(a) + f(b) 2 . which provides estimates of the mean value of a convex function f on [a, b] where μ is the Lebesgue measure on R. This inequality in general, is not valid in the fuzzy context. In this paper, we find necessary and sufficient conditions of Hermite-Hadamard type inequality f...

The aim of this paper is to establish some new Hermite–Hadamard type inequalities for harmonic h-convex functions involving hypergeometric functions. We also discuss some new and known special cases, which can be deduced from our results. The ideas and techniques of this paper may inspire further research in this field. In recent years, much attention have been given to theory of convexity beca...

Abstract In this paper, we have established some generalized inequalities of Hermite–Hadamard–Fejér type for integrals. The results obtained are applied fractional integrals various and therefore contain previous reported in the literature.

Abstract In this paper, we establish Jensen’s inequality for s -convex functions in the first sense. By using inequalities, obtain some Cauchy type means p and Also, by Hermite–Hadamard inequalities respective generalized convex functions, find new means.

In the paper, we study dynamic h-convexity for interval valued functions. Some generalizations of Jensen’s inequality in analysis h-convex functions on time scales are proved paper. seek applications generalized inequality, Hermite-Hadamard type inequalities established. Further discrete analogues newly results also presented numerical examples provided to check validity results.

In this study, we investigated the general convexity of functions which is named preinvexity. Firstly, generalized Hermite-Hadamard type integral inequality for two-dimensional preinvex functions. Then, obtained a generalization Ostrowski Besides, derived some new inequalities related to these