FEJÉR-HERMITE-HADAMARD TYPE PROPERTIES OF GENERALIZED (h,m)-EXPONENTIALLY CONVEX FUNCTIONS ON FRACTAL SETS

In this article, we introduce the class of generalized $(h,m)$-exponentially convex functions on fractal sets ($\mathbb{R}^{\alpha}, 0 <\alpha \leq1$), an extension of the category of generalized $(h-m)$-convex functions and consequently prove new Hermite-Hadamard type and Fej\'er-Hermite-Hadamard type integral properties of these mappings. Additionally, we deduce specific inequalities concerning $h$-convexity and exponential $(h, m)$-convexity, which arise as particular cases in our analysis. To verify the accuracy of the current findings, we also examine some novel applications for generalized special means.