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

Xinlin Zhan, Abdul Mateen, Muhammad Toseef and Muhammad Aamir Ali ()
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Xinlin Zhan: School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
Abdul Mateen: Ministry of Education Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
Muhammad Toseef: Ministry of Education Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
Muhammad Aamir Ali: Ministry of Education Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China

Mathematics, 2024, vol. 12, issue 11, 1-23

Abstract: Integral inequalities are very useful in finding the error bounds for numerical integration formulas. In this paper, we prove some multiplicative integral inequalities for first-time differentiable s -convex functions. These new inequalities help in finding the error bounds for different numerical integration formulas in multiplicative calculus. The use of s -convex function extends the results for convex functions and covers a large class of functions, which is the main motivation for using s -convexity. To prove the inequalities, we derive two different integral identities for multiplicative differentiable functions in the setting of multiplicative calculus. Then, with the help of these integral identities, we prove some integral inequalities of the Simpson and Ostrowski types for multiplicative generalized convex functions. Moreover, we provide some numerical examples and computational analysis of these newly established inequalities, to show the validity of the results for multiplicative s -convex functions. We also give some applications to quadrature formula and special means of real numbers within the framework of multiplicative calculus.

Keywords: Simpson’s inequality; Ostrowski’s inequality; multiplicative calculus; multiplicatively convex function; multiplicatively s-convex function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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