On Some Characterization of GS-exponential kind of Convex Functions

TL;DR

This paper introduces GS-exponential convex functions and sets, exploring their algebraic properties, fundamental characteristics, and conditions for optimality in unconstrained and constrained programming contexts.

Contribution

It presents a new class of GS-exponential convex functions and sets, along with their algebraic features and optimality conditions, expanding the theory of convex analysis.

Findings

Defined GS-exponential convex functions and sets

Established algebraic properties and characteristics

Derived sufficient optimality conditions for programming problems

Abstract

This manuscript introduces the idea of GS-exponential kind of convex functions and some of their algebraic features, and we introduce a new class GS-exponential kind of convex sets. In addition, we describe certain fundamental GS-exponential kind of convex function with characteristics in both the general and the differentiable cases. We establish the sufficient conditions of optimality and offer the proof for unconstrained as well as inequality-constrained programming while considering the assumption of GS-exponential kind of convexity.