严格F-G广义凸函数

Strictly F-G Generalized Convex Functions

给出一类新的广义凸函数——严格F-G广义凸函数,并给出条件P1、P2及其性质,研究严格F-G广义凸函数的若干性质,给出严格F-G广义凸函数的两个充分条件,指出在一定条件下,满足中间点严格F-G广义凸性的F-G广义凸函数是严格F-G广义凸函数,满足中间点严格F-G广义凸性的半严格F-G广义凸函数是严格F-G广义凸函数.最后给出严格F-G广义凸函数在极小化问题中的一个实际应用.

This paper gives a new class of generalized convex functions-strictly F-G generalized convex functions, and the conditions P1, P2 as well as their properties. It studies on the properties of strictly F-G generalized convex functions, gives two sufficient conditions of strictly F-G generalized convex functions, and points out that under certain conditions, F- G generalized convex functions which satisfies intermediate-point strictly FG generalized convexity is strictly F-G generalized convex functions, and semi-strictly F-G generalized convex functions which satisfies intermediate-point strictly F-G generalized convexity is strictly F-G generalized convex functions. And the paper provides a realistic application of strictly F- G generalized convex functions in minimization problem.