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...

In this paper, the author introduces the concept of the quasi-geometrically convex functions, gives Hermite-Hadamard’s inequalities for GA-convex functions in fractional integral forms and defines a new identity for fractional integrals. By using this identity, the author obtains new estimates on generalization of Hadamard et al. type inequalities for quasi-geometrically convex functions via Ha...

In this paper we prove some inequalities for convex function of a higher order. The well known Hermite interpolating polynomial leads us to a converse of Jensen inequality for a regular, signed measure and, as a consequence, a generalization of Hadamard and Petrovi c's inequalities. Also, we obtain a new upper bound for the error function of the Hermite interpolating polynomial je H (x)j in ter...

In this paper, we establish some new quantum Hermite-Hadamard type inequalities for differentiable convex functions by using the q?2-quantum integral. The results presented in paper extend of Bermudo et al. (On q-Hermite-Hadamard general functions, Acta Mathematica Hungarica, 2020, 162, 363-374). Finally, give examples to show validation paper.

This article is organized as follows: First, definitions, theorems, and other relevant information required to obtain the main results of are presented. Second, a new version Hermite–Hadamard inequality proved for F-convex function class using fractional integral operator introduced by Katugampola. Finally, Hermite–Hadamard-type inequalities given with help F-convexity.

The well-known Hermite-Hadamard integral inequality was established by Hermite at the end of 19th century (see [1]). There are many recent contributions to improve this inequality, please refer to [2,3,4,5,6] and references therein. It is worth noting that there are some interesting results about Hermite-Hadamard inequalities via fractional integrals according to the corresponding integral equa...

In this paper, we prove the Hermite–Hadamard–Fejér type inequalities for coordinated h1,h2-convex functions on rectangle from plane R2. Some generalizations of Hermite–Hadamard-type two variables are also obtained as a consequence. properties functionals which connected with provided well. Finally, give applications acquired results to special means positive real numbers.