On some characterizations of generalized s-convex functions

Generalized [Formula: see text]-convex functions are a new class of generalized convex functions that have been established in this paper. In a similar sense, a new class of generalized [Formula: see text]-convex sets is introduced as a generalization of [Formula: see text]-convex sets. Additionally, a number of fundamental characteristics of generalized [Formula: see text]-convex functions are investigated, both for general and differentiable cases. Furthermore, adequate criteria for optimality are defined for both unconstrained and inequality-constrained programming, and this is demonstrated using generalized [Formula: see text]-convexity.