Some Characterizations of General s-Convex Functions

It is established that the general s-Convex function are a new class of generalized 
convex functions. In a similar ven a new class of general s-convex sets is introduced which 
are generalizations of s-convex set. It is shown that radially lower semicontinuous function 
 * + is general s-convex if and only if , for all there exist 𝜎 
( 
) ( ) that satisfies
 (𝜎 ( 𝜎) 
) 𝜎
 
[( ( 
)) ( 𝜎)] ( 𝜎)
 
, ( 
) ( 𝜎)- 
 .
 
 
 𝜎/ 
holds 𝜎 , - and for some fixed ( -.