Perturbed proximal point algorithms for general quasi-variational-like inclusions

In this paper, we introduce two new concepts of eta-subdifferential and eta-proximal mappings of proper functionals on Hilbert spaces. The existence and Lipschitz continuity of eta-proximal mapping of a proper functional are proved. By applying these concepts, we introduce and study a class of general quasi-variational-like inclusions and develop some new perturbed eta-proximal point algorithms of Mann and Ishikawa type for finding the approximate solutions of the general quasi-variational-like inclusions. The convergence criteria of the sequences of approximate solutions generated by these new algorithms are also discussed. Our algorithms and results improve and generalize many known results in the literature. (C) 2000 Elsevier Science B.V. All rights reserved. MSC. 49J40; 47H19; 47H10.