  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.
