  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.
