Bounds for the Remainder in Simpson’s Inequality vian-Polynomial Convex Functions of Higher Order Using Katugampola Fractional Integrals

Abstract

The goal of this paper is to derive some new variants of Simpson’s inequality using the class of n-polynomial convex functions of higher order. To obtain the main results of the paper, we first derive a new generalized fractional integral identity utilizing the concepts of Katugampola fractional integrals. This new fractional integral identity will serve as an auxiliary result in the development of the main results of this paper.

Integral inequalities for n‐polynomial s‐type preinvex functions with applications

“…The remarkable ideas of this article may motivate for further research and useful to generate the Mandelbrot and Julia sets for quadratic and cubic polynomial with s ‐convexity 17,18 . For the recent literature about the generalization of convexity and inequalities, see the references in the literature 19–23 …”

“…17,18 For the recent literature about the generalization of convexity and inequalities, see the references in the literature. [19][20][21][22][23] The main aim and principal focus of this paper is to define and introduce the concept of n-polynomial s-type preinvex functions. In addition, we show that the algebraic properties of newly introduced definition and discuss their connections and relations with previous published literature about convex functions.…”

Strongly n-polynomial convexity and related inequalities

“…See articles [14,17,19,23,27] and the references therein. We would also like to point out in particular that readers wishing to learn more about the subject of this article and the various types of convexity may refer to the references [3,1,2,4,6,7,9,10,8,11,24,20,21,25,26,29,28,30,31,33].…”

Ostrowski-type inequalities for n-polynomial $\mathscr{P}$-convex function for k-fractional Hilfer–Katugampola derivative

“…China. 3 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, 410114, P.R. China.…”

“…Fragmentary necessary conditions incorporate a derivative of any unpredictable or real requirement, which will likewise be viewed as differing conditions of an overall sort. Many explorations are considered having been proposed to upgrade demonstrating the accuracy while indicating the diffusion process, displaying various types of viscoelastic damping, unequivocally leading to the reliance on power-law frequencies, and modeling fragmentary Maxwell liquid streaming (see [3,5,20]).…”