Fej\'er-Hermite-Hadamard type properties of generalized $(h,m)$-exponentially convex functions on fractal sets
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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.
Abstract
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.