holds. This double inequality is known in the literature as Hermite-Hadamard integral inequality for convex functions. Note that some of the classical inequalities for means can be derived from (1.1) for appropriate particular selections of the mapping f . Both inequalities hold in the reversed direction if f is concave. For some results which generalize, improve and extend the inequalities (1....

The Hermite-Hadamard inequality has been recognized as the most pivotal which grabbed attention of several mathematicians. In recent years, load results have established for this inequality. main theme article is to present generalized via Jensen-Mercer and majorization concept. We establish a type majorized tuples. With aid weighted Mercer?s inequality, we also prove certain idea obtaining pap...

Abstract In both theoretical and applied mathematics fields, integral inequalities play a critical role. Due to the behavior of definition convexity, concepts convexity inequality depend on each other. Therefore, relationship between symmetry is strong. Whichever one we work on, introduced new class generalized convex function known as LR- $$\left({h}_{1}, {h}_{2}\right)$$ <mml:math xmlns:mml="...

We establish some estimates of the right-hand side of Hermite-Hadamard type inequalities for functions whose derivatives absolute values are harmonically s-convex. Several Hermite-Hadamard type inequalities for products of two harmonically s-convex functions are also considered.

Abstract In this work, we established some new general integral inequalities of Hermite–Hadamard type for s -convex functions. To obtain these inequalities, used the Hölder inequality, power-mean and generalizations associated with inequalities. Also compared (e.g., Theorem 6 8). Finally, gave applications special means.

In this paper, by using Jensen–Mercer’s inequality we obtain Hermite–Hadamard–Mercer’s type inequalities for a convex function employing left-sided (k, ψ)-proportional fractional integral operators involving continuous strictly increasing function. Our findings are generalization of some results that existed in the literature.

The term convexity associated with the theory of inequality in sense fractional analysis has a broad range different and remarkable applications domain applied sciences. prime objective this article is to investigate some new variants Hermite–Hadamard Pachpatte-type integral inequalities involving idea preinvex function frame operator, namely Caputo–Fabrizio operator. By employing our approach,...

In this manuscript, we introduce concepts of (m1,m2)-logarithmically convex (AG-convex) functions and establish some Hermite-Hadamard type inequalities of these classes of functions.

Abstract There are a lot of papers dealing with applications the so-called cyclic refinement discrete Jensen’s inequality. A significant generalization refinement, based on combinatorial considerations, has recently been discovered by author. In present paper we give integral versions these results. On one hand, new method to refine inequality is developed. other result contains some recent ref...