STABLE PERTURBED PROXIMAL POINT ALGORITHM FOR GENERALIZED STRONGLY NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS

Abstract

In this paper, we introduce and study a new class of generalized strongly nonlinear quasi-variational-like inclusions. By using the proximal mapping technique for subdifferential of the proper convex lower semi-continuous functional introduced by Ding and Luo [5], and Lee et al. [16], we construct a new perturbed iterative algorithm with errors for solving this kind of generalized strongly nonlinear quasi-variational-like inclusions. We also discuss the convergence and stability of the iterative sequence generated by the algorithm. The results presented in this paper extend and improve many known results.