Generalization of some integral inequalities in multiplicative calculus with their computational analysis

Abdul Mateen; Zhiyue Zhang; Muhammad Aamir Ali; Michal Fečkan

doi:10.3842/umzh.v76i10.7765

Abdul Mateen Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
Zhiyue Zhang Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
Muhammad Aamir Ali Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China
Michal Fečkan Department of Mathematical Analysis and Numerical Analysis, Comenius University in Bratislava, Slovakia, and Institute of Mathematics, Slovak Academy of Sciences, Bratislava, Slovakia

DOI: https://doi.org/10.3842/umzh.v76i10.7765

Keywords: Hermite-Hadamard Inequality, Simpson’s Inequality, Bullen’s Inequality, Multiplicative Calculus, Multiplicatively Convex Function

Abstract

UDC 517.9

We focus on generalizing some multiplicative integral inequalities for twice differentiable functions. First, we derive a multiplicative integral identity for multiplicatively twice differentiable functions. Then, with the help of the integral identity, we prove a family of integral inequalities, such as Simpson, Hermite–Hadamard, midpoint, trapezoid, and Bullen types inequalities for multiplicatively convex functions. Moreover, we provide some numerical examples and computational analysis of these newly established inequalities to prove the validity of the results for multiplicatively convex functions. The generalized forms obtained in our research offer valuable tools for researchers in various fields.

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