Generalized quasi-variational-like inclusions with nonconvex functionals

摘要

In this paper, two new concepts of η-subdifferential and η-proximal mappings of a proper functional is introduced in Hilbert spaces. The existence and Lipschitz continuity of η-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 convergence criteria of the iterative sequences generated by the algorithm are also given. These algorithm and existence result generalize many known results in the literature.