Generalized Fractal‐Fractional Mercer Variants of Hermite‐Hadamard‐Fejér and Pachpatte Type Inequalities for Harmonically h‐Convex Functions Involving Mittag‐Leffler Kernel With Applications

ABSTRACT In this study, we first time introduce a class of generalized harmonically ‐convex functions on fractal sets and present generalized Jensen and Jensen‐Mercer inequality for this class. By utilizing a generalized harmonically ‐convex function, we establish new fractal Hermite‐Hadamard‐Mercer type inequalities via fractional integral operators pertaining to the Mittag‐Leffler function in the kernel. We also provide the fractal Mercer variants of inequalities of Pachpatte's and Hadamard‐Fejér's type for generalized harmonically ‐convex functions. We give an example that shows tighter lower bounds. Visual illustrations show the accuracy and supremacy of the modified technique. We established a new proof of the Hölder Yang's inequality utilizing generalized Jensen inequality for harmonically convex functions. Finally, the validity of the obtained results leads us to generate generalized special fractal means. The new results clearly provide extensions and improvements of the work given in literature.