Simpson’s Type Estimates for Multiplicatively Strongly Convex Function via Non-Newtonian Calculus

Abstract

In this paper, we initially establish a novel integral identity for multiplicatively differentiable functions within the framework of non-Newtonian calculus. By judiciously exploiting this identity, we derive a new Simpson’s-type integral inequality for multiplicatively strongly convex functions. Several significant special cases and particular instances of the principal result are subsequently examined, thereby demonstrating the breadth and versatility of the proposed framework. Furthermore, illustrative applications involving various special means are presented to substantiate the analytical significance of the obtained results. The findings contribute to and substantially extend the existing theory of multiplicative integral inequalities by providing a unified analytical framework for the investigation of Simpson’s estimates in non-Newtonian calculus. The newly established identity constitutes a powerful analytical instrument that may serve as a foundation for deriving further integral inequalities associated with broader classes of multiplicatively strongly convex functions and related generalized convexity structures.