On Some Characterizations of General s-Convex Functions

TL;DR

This paper introduces and characterizes a new class of general s-convex functions and sets, exploring their fundamental properties and applications in optimization problems.

Contribution

It defines general s-convex functions and sets, analyzes their properties, and establishes optimality criteria in unconstrained and constrained programming.

Findings

General s-convex functions form a new class of generalized convex functions.

Fundamental properties of general s-convex functions are discussed.

Sufficient optimality criteria are established for various programming problems.

Abstract

It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain fundamental characteristics of general s-convex functions are discussed for both general cases and differentiable situations. Aside from that, the general s-convexity is used to define and demonstrate the sufficient criteria for optimality for both unconstrained and inequality-constrained programming.