A novel comprehensive analysis of the refinements of Hermite-Hadamard type integral inequalities involving special functions

Abstract

The main objective of this article is to employ the concept of preinvexity to establish some new inequalities. In addition, we discuss some algebraic properties and examples of the generalized preinvex function. With the help of this new relation, we present new version of Hermite-Hadamard inequality and its some of its refinements using fundamental inequalities like H ölder, power-mean, H ölder-˙Iscan, and improved power-mean inequality. These results are speculations of various recently known outcomes. The immeasurable concepts and tools of this paper may invigorate and revitalize for additional research in this mesmerizing and absorbing field.

Error Bounds for Fractional Integral Inequalities with Applications

“…It has a simple geometriciexplanation and several applications. See these articles [21][22][23] for more information on the Hermite-Hadamard type inequalities. Budak et al has established Hermite-Hadamard type inequalities using Riemann-Liouvilleifractional integrals (see [24]).…”

New Versions of Midpoint Inequalities Based on Extended Riemann–Liouville Fractional Integrals

“…The inequality of Hermite-Hadamard is the first result of convex mappings, and has a straightforward geometric demonstration and a variety of applications, making it the most interesting inequality. For more details concerning the Hermite-Hadamard inequality, see [13][14][15]. Using Riemann-Liouville fractional integrals and convex analysis, Sarikaya et al [16] recently proved many Hermite-Hadamard and trapezoidal inequalities.…”

On New Fractional Version of Generalized Hermite-Hadamard Inequalities

“…The inequalities found by Hermite and Hadamard for convex mappings are frequently considered in mathematical literature (see [1][2][3] and [4] (p. 137)). These inequalities explain that if ξ is a convex mapping from the interval J into R and ϑ 1 , ϑ 2 ∈ J with ϑ 1 < ϑ 2 , then…”

“…During the past few decades, many papers have focused on generalizing inequalities of the trapezoid and midpoint types, which provide limits for the two sides of inequality (1). Trapezoid and midpoint inequalities for convex functions were first derived by the authors in [10,11], respectively.…”