Explicitly B-preinvex functions

This paper introduces a new class of functions, to be referred to as explicitly B-preinvex functions. Some properties of explicitly B-preinvex functions are established, e.g., any local minimum of an explicitly B-preinvex function is also a global one and the summation of two functions, which are both B-preinvex and explicitly B-preinvex, is also a B-preinvex function and an explicitly B-preinvex function. Furthermore, it is shown that the explicit B-preinvexity, together with the intermediate-point B-preinvexity, implies B-preinvexity, while the explicit B-preinvexity, together with a lower semicontinuity, implies the B-preinvexity.