Semi-strictly F-G Generalized Convex Functions

This paper defines generalized convex sets and generalized convex functions,furthermore gives the definition of Semi-strictly F-G generalized convex functions.It generalizes the conditions C of reference[5] to conditions P1,P2,gives their properities and obtains the equal relation between conditions P1 and P2.The relation is supposed F to satisfy conditions P1 and P2 over K,then for any λ∈(0,1)and for any u1,u2∈,u1≠u2,then for all x,y∈K,we have F(x,y,λu1+(1-λ)u2)=F[F(x,y,u1),F(x,y,u2),λ].Based on this,comparing to reference[9] and ,the author gives two sufficient conditions of semi-strictly F-G generalized convex functions and gives that under certain conditions,F-G generalized convex functions is semi-strictly F-G generalized convex functions when F-G generalized convex functions satisfy intermediate-point semi-strictly F-G generalized convexity.At last,this paper enumerates several vector valued functions F and numerical functions G and the applications of semi-strictly F-G generalized convex functions in minimization problems.