Generalization of Some Integral Inequalities in Multiplicative Calculus With Their Computational Analysis

Abstract

This paper focuses on the generalization of some multiplicative integral inequalities for twice differentiable functions. First, we derive multiplicative integral identity for multiplicatvely twice differentiable functions. Then, with the help of integral identity, we prove a family of integral inequalities such that Simpson’s, Hermite-Hadamard, Midpoint, Trapezoid and Bullen’s types inequalities for multiplicatively convex functions. Moreover, we provide some numerical examples and computational analysis of these newly established inequalities to show the validity of the results for multiplicatively convex functions. The generalized forms derive in this research offer valuable tools for researchers in various fields. 2010 Mathematics Subject Classification. 34A08, 26A51, 26D15.

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:…”