NEW NEWTON'S TYPE ESTIMATES PERTAINING to LOCAL FRACTIONAL INTEGRAL VIA GENERALIZED p -CONVEXITY with APPLICATIONS

Abstract

This paper aims to investigate the notion of p-convex functions on fractal sets α(0 < α ≤ 1). Based on these novel ideas, we derived an auxiliary result depend on a three-step quadratic kernel by employing generalized p-convexity. Take into account the local fractal identity, we established novel Newton's type variants for the local differentiable functions. Several special cases are apprehended in the light of generalized convex functions and generalized harmonically convex functions. This novel strategy captures several existing results in the relative literature. Application is obtained in cumulative distribution function and generalized special weighted means to confirm the relevance and computational effectiveness of the considered method. Finally, we supposed that the consequences of this paper can stimulate those who are interested in fractal analysis. © 2021 The Author(s).