On m-Exponential Convexity with Respect to s and Its Applications

Abstract

The concept of convexity represents one of the fundamental notions of mathematical analysis and optimization. Various extensions of the concept of convexity have contributed to a wide range of applications, including the study of integral inequalities, approximation theory, and other areas of applied mathematics. In this paper, we start from exponentially convex functions defined with respect to $s$ and introduce a new class of $m$-exponentially convex functions with respect to $s$. Furthermore, the basic algebraic properties of this class are analyzed. In the second part, special attention is devoted to the application and the meaning of the extension of the Hermite–Hadamard inequality, where a more general framework is provided compared to the existing ones. The obtained results, in addition to their theoretical significance, also point to the potential for applications in data analysis, optimization, and further generalizations.