Some characterizations and applications on strongly $\alpha$-preinvex and strongly $\alpha$-invex functions
Cai-Ping Liu · Journal of Industrial and Management Optimization · 2008
In this paper, a new class of generalized convex functions isintroduced, which is called the strongly quasi $\alpha$-preinvexfunctions. Some properties of strongly $\alpha$-preinvex functionsare studied. We establish the relationships among the strongly quasi$\alpha$-preinvex functions, strongly quasi $\alpha$-invex functionsand strongly quasi $\alpha\eta$-monotonicity under some suitableconditions. As applications, a class of perturbed variational-likeinequality problems is introduced, some relationships between theperturbed variational-like inequality andoptimization problems are established under the assumptions of strongly $\alpha$-invex functions.