New Simpson Type Integral Inequalities for $s$-Convex Functions and Their Applications

Abstract

First, we consider a new Simpson’s identity. This identity investigates our main results that consist of some integral inequalities of Simpson’s type for the s –convex functions. From our main results, we obtain some special cases which are discussed in detail. Finally, some applications on the Bessel functions, special means of distinct positive real numbers, and error estimation about Simpson quadrature formula are presented to support our theoretical results.

Parameterized Simpson-like inequalities for differentiable Bounded and Lipschitzian functions with application example from management science

“…Over the past few decades, a considerable body of literature has delved into the investigation of error estimations for Simpson-type formulas for a diverse range of function classes, including but not limited to convex functions, bounded functions, and other such classes. (see [Ali et al 2021;Alomari and Darus 2010;Budak et al 2021;Chiheb et al 2020;Erden et al 2020;Hezenci et al 2021;Kara et al 2022;Kashuri et al 2020;Kashuri et al 2021;Lakhdari and Meftah 2022;Meftah et al 2023;Rostamian Delavar et al 2021;Saleh et al 2023;Yang and Tseng 2001;You et al 2022]) This paper focuses on 4-point Newton-Cotes type inequalities. The most renowed inequalities related to this type of formula is the second Simpson's quadrature formula called 3/8-Simpson rule or closed Newton-Cotes four-point formula which can be stated as follows:…”

Maclaurin-Type Integral Inequalities for GA-Convex Functions Involving Confluent Hypergeometric Function via Hadamard Fractional Integrals

“…Their aim has been to develop new refinements, generalizations, and variants. For additional details, readers are encouraged to consult references [1][2][3][4][5][6][7][8][9][10] for classical inequalities, and [11][12][13][14] for fractional inequalities.…”

Fractional Simpson-like Inequalities with Parameter for Differential s-tgs-Convex Functions

“…Convexity has a close relation in the development of the theory of inequalities, of which it plays an important role in the study of qualitative properties of solutions of ordinary, partial, and integral differential equations as well as in numerical analysis, which is used for establishing the estimates of the errors for quadrature rules; see [7][8][9][10][11][12][13][14][15][16][17][18].…”