New “Conticrete” Hermite–Hadamard–Jensen–Mercer Fractional Inequalities

Abstract

The theory of symmetry has a significant influence in many research areas of mathematics. The class of symmetric functions has wide connections with other classes of functions. Among these, one is the class of convex functions, which has deep relations with the concept of symmetry. In recent years, the Schur convexity, convex geometry, probability theory on convex sets, and Schur geometric and harmonic convexities of various symmetric functions have been extensively studied topics of research in inequalities. The present attempt provides novel portmanteauHermite–Hadamard–Jensen–Mercer-type inequalities for convex functions that unify continuous and discrete versions into single forms. They come as a result of using Riemann–Liouville fractional operators with the joint implementations of the notions of majorization theory and convex functions. The obtained inequalities are in compact forms, containing both weighted and unweighted results, where by fixing the parameters, new and old versions of the discrete and continuous inequalities are obtained. Moreover, some new identities are discovered, upon employing which, the bounds for the absolute difference of the two left-most and right-most sides of the main results are established.

New Majorized Fractional Simpson Estimates

“…Taking into account the above notable Niezgoda inequality, Faisal et al [21] recently introduced the below-mentioned Hermite-Hadamard-type inequality for majorized tuples:…”

Hermite–Hadamard and Jensen‐Type Inequalities via Riemann Integral Operator for a Generalized Class of Godunova–Levin Functions

“…It is well known that the convexity of functions plays an extremely important role in mathematics and other scienti c elds such as economics, probability theory, and optimal control theory; moreover, several inequalities have been recorded in the literature (see [13][14][15][16][17]). In equality, the following inequality is called a classical Hermite-Hadamard inequality:…”

Simpson Type Conformable Fractional Inequalities

“…Often, one can solve a mathematical problem, by estimating an answer, rather than writing down exactly what it is. For more information in this regard, one can see [1][2][3][4][5][6][7][8].…”