Generalized quasi-variational-like inclusions with nonconvex functionals

In this paper, two new concepts of eta -subdifferential and eta -proximal m appings of a proper functional is introduced in Hilbert spaces. The existen ce and Lipschitz continuity of eta -proximal mapping of a proper functional are proved. By applying these concepts, we introduce and study a class of generalized quasi-variational-like inclusions with a nonconvex functional. A new iterative algorithms for finding the approximate solutions and the co nvergence criteria of the iterative sequences generated by, the algorithm a re also given. These algorithm and existence result generalize many known r esults in the literature. (C) 2001 Elsevier Science Inc. All rights reserve d.