THE MULTI-PARAMETER FRACTAL–FRACTIONAL INEQUALITIES FOR FRACTAL (P,m)-CONVEX FUNCTIONS

Abstract

Local fractional calculus theory and parameterized method have greatly assisted in the advancement of the field of inequalities. To continue its enrichment, this study investigates the multi-parameter fractal–fractional integral inequalities containing the fractal $(P,m)$-convex functions. Initially, we formulate the new conception of the fractal $(P,m)$-convex functions and work on a variety of properties. Through the assistance of the fractal–fractional integrals, the $2\ell$-fractal identity with multiple parameters is established, and from that, integral inequalities are inferred regarding twice fractal differentiable functions which are fractal $(P,m)$-convex. Furthermore, a few typical and novel outcomes are discussed and visualized for specific parameter values, separately. It concludes with some applications in respect of the special means, the quadrature formulas and random variable moments, respectively.