B-(E,F)-凸函数及其性质

B-(E,F)-convex function and the properties

引入一类新的广义凸函数B-(E,F)-凸函数,进一步弱化了现有几类广义凸函数,使得B-凸函数、E-凸函数和(E,F)-凸函数等成为B-(E,F)-凸函数的特例,研究了这类函数的相关性质,得到一些重要结论,同时得出B-(E,F)-凸函数为(E,F)-凸函数和凸函数的充分条件.

In this paper, a new class of generalized convex function B--（E,F）--convex function is introduced. The convexity of several kind generalized convex functions is weakened, so B--convex function; E--convex function and （E,F）--convex function become a special case of the B--（E,F）-- convex function. Some basic characters of these functions are researched and important results are given; meanwhile, the sufficient conditions that B--（E,F）- convex function is （E, F）- convex function and B--（E, F）--convex function are obtained.