The F-G Generalized Convex and F Quasi Convex Functions

Given in this paper are the definitions of F-G generalized convex functions,F quasi convex functions and their examples.By using the conditions P1 and P2,the author gives some properties of F-G generalized convex functions,gives functions Φ(λ)=f[F(x,y,λ)] which was made by F-G generalized convex functions be(quasi) convex function on ,gives Sη(f)={xx∈K,f(x)≤η} is generalized convex sets about F and gives f is F-G generalized convex functions over K if and only if f is F-G approximately generalized convex functions and F quasi convex functions over K.At last,the author gives the applications of semi-strictly F quasi convex functions in minimization problem and gives when limλ→0F(x,y,λ)=y,then local optimal solution of semi-strictly F quasi convex functions is global optimal solution.