A novel perspective on the Bullen and Milne inequalities through the use of multiplicatively absolute value

Abstract

This article formulates a new version to multiplicative Bullen and Milne inequalities
derived from constraints on multiplicative Riemann-Liouville fractional integrals.
We establish these further inequalities under the multiplicative absolute value
and on the assumption that the function is multiplicatively h-convex.
Additionally, these results are presented for multiplicatively P-functions and
multiplicatively s-convex functions. The final section introduces a novel definition
of a multiplicative Lipschitzian function, accompanied by examples, properties and theorems.