(𝓹,𝔼)-convex sets and (𝓹,𝔼)-Convex functions with their properties

Abstract

In this paper, new classes of (𝓅,𝔼) −convex sets and (𝓅,𝔼) −convex functions are presented by combining the classes of 𝓅-convexity and 𝔼-convexity of sets and functions, respectively. Various non-trivial examples of the new set and function are constructed and their relationships with 𝓅-convex sets and functions (respectively, 𝔼-convex sets and functions) are shown. Some basic and important properties of (𝓅,𝔼) −convex sets and functions are discussed.