Generalized p -Convex Inequalities on Fractal Sets with Neural Network Modeling

Abstract

In this article, we developed a new variant of discrete Jensen-type inequality for p-convex functions over fractal sets. Improvement and generalization of some Jensen-Mercer-type estimates for [Formula: see text]-convex function in the framework of fractal fractional calculus are obtained. Using this Jensen-Mercer inequality, we establish a Hermite-Hadamard-Mercer (HHM) type inequalities for [Formula: see text]-convex functions in fractal dimensions. We drive a new integral identity and HHM type inequalities for differentiable [Formula: see text]-convex functions. Some of the results presented here for [Formula: see text]-convex functions are extensions of earlier results for harmonically convex and convex functions. Finally, we also provide a neural network-based numerical analysis of the obtained results, showing the accuracy and effectiveness of the proposed inequalities for [Formula: see text]-convex functions.