Characterizations and Applications of Quasi A-Preinvex Functions

In this paper, one important type of generalized convex functions termed as strongly quasi α-preinvex functions is studied. The relationships among strongly quasi α-preinvex functions, quasi α-preinvex functions, strictly quasi α-preinvex functions and semi strictly quasi α-preinvex functions have been discussed. Three important theorems of properties have been obtained for it on the middle point strongly quasi α-preinvexity. Finally, strongly quasi α-preinvex functions are used in the study of optimization problems.