This study deals with a novel class of mean-type inequalities by employing fractional calculus and convexity theory. The high correlation between symmetry increases its significance. In this paper, we first establish an identity that is crucial in investigating mean inequalities. Then, the main results involving error estimation Hermite–Hadamard inequality for composite convex functions via gen...

Abstract In this article we give two possible generalizations of the Hermite–Hadamard integral inequality for class twice differentiable functions, where convexity property target function is not assumed in advance. They represent a refinement case convex/concave functions with numerous applications.

equality holds in either side only for the affine functions (i.e., for the functions of the form mx+ n). The middle point (a + b)/2 represents the barycenter of the probability measure 1 b−adx (viewed as a mass distribution over the interval [a, b]), while a and b represent the extreme points of [a, b]. Thus the Hermite-Hadamard inequality could be seen as a precursor of Choquet’s theory. See [...

Some sharp trapezoid and midpoint type inequalities for Lipschitzian bifunctions defined on a closed disk in Euclidean sense are obtained by the use of polar coordinates. Also, whose partial derivative is considered. A new presentation Hermite-Hadamard inequality convex function its reverse given. Furthermore, two mappings H <mf...

In this work, we introduce the idea of n –polynomial harmonically id="M4"> s –type convex function. We elaborate new introduced by examples and some interesting algebraic properties. As a result, Hermite–Hadamard, refinements Hermite–Hadamard Ostrowski type integral inequalities are established, which generalize...

In order to be able study cosmic phenomena more accurately and broadly, it was necessary expand the concept of calculus. this study, we aim introduce a new fractional Hermite–Hadamard–Mercer’s inequality its integral type inequalities. To facilitate that, use proportional operators integrable functions with respect another continuous strictly increasing function. Moreover, establish some weight...