Some New Simpson’s-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators

Abstract

From the past to the present, various works have been dedicated to Simpson’s inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity involving twice-differentiable functions, then we use this result to prove some new Simpson’s-formula-type inequalities for twice-differentiable convex functions. Furthermore, we examine a few special cases of newly established inequalities and obtain several new and old Simpson’s-formula-type inequalities. These types of analytic inequalities, as well as the methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.

Some Simpson-like Inequalities Involving the (s,m)-Preinvexity

“…As the above inequalities are very popular in estimating errors of quadrature rules, many researchers have massively studied them, as well as similar inequalities; one can consult, for example, [21][22][23][24][25][26][27][28][29][30] and references therein.…”

Some Simpson- and Ostrowski-Type Integral Inequalities for Generalized Convex Functions in Multiplicative Calculus with Their Computational Analysis

“…For some results regarding inequality (6) and related inequalities, one can consult [17][18][19][20]. Ali et al obtained some Simpson-and Ostrowski-type inequalities in the context of multiplicative integrals in [6], as follows:…”

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:…”