Hermite-hadamard type inequalities for generalized $s$-convex functions on real linear fractal set $\mathbb{R}^{\alpha}(0<\alpha<1)$

TL;DR

This paper extends Hermite-Hadamard inequalities to generalized s-convex functions defined on real linear fractal sets, providing new bounds and inequalities in the context of fractal geometry and fractional calculus.

Contribution

It introduces Hermite-Hadamard type inequalities for generalized s-convex functions on fractal sets, expanding classical inequalities into fractal and fractional frameworks.

Findings

Established Hermite-Hadamard inequalities for generalized s-convex functions on fractal sets

Extended classical convexity inequalities to fractional and fractal contexts

Provided new bounds for functions on $ ext{R}^ ext{alpha}$ with $0< ext{alpha}<1$

Abstract

In the paper, we establish the Hermite-Hadamard type inequalities for the generalized s-convex functions in the second sense on real linear fractal set $\mathbb{R}^{\alpha}(0<\alpha<1).$