THREE FRACTIONAL INEQUALITIES BASED ON A SINGLE PARAMETER IN THECONTEXT OF AG-MULTIPLICATIVE h-CONVEX FUNCTIONS

Abstract

Abstract. This article introduces novel three parameterized fractional inequalities based on a one parameter ν derived from functions that are AG-multiplicative differentiable, as characterized by AG-multiplicatively Riemann-Liouville operators (classical, middle starting point, and middle ending point). By employing the multiplicative absolute value and supposing the function is AG-multiplicative h-convex, we can develop three identities and utilize them to derive a series of inequalities for AG-multiplicatively h-convex mappings. We additionally present these findings for AG-multiplicative P-functions convex mapping and AG-multiplicative s-convex functions. The last section delineates specific  instances, including trapezoid, midpoint, Bullen, Milne, Simpson and corrected Simpson AG-multiplicative fractional inequalities. We further illustrate that certain results reported here improve established results, while others represent generalizations.
Keywords: Parameterized inequality, AG-multiplicative fractional integrals, Multiplicative absolute value, AG-multiplicative h-convex functions