Bounded perturbation resilience of generalized viscosity iterative algorithms for split variational inclusion problems

Abstract

In this paper, we propose a generalized viscosity approximation method combing a sequence of contractive mappings to solve a split variational inclusion problem. The bounded perturbation resilience of the method is investigated in Hilbert spaces. Under mild conditions, we prove that our algorithms strongly converge to a solution of the split variational inclusion problem, which is also the unique solution of some variational inequality problem. Furthermore, we show the convergence and effectiveness of the algorithms via two numerical examples. Our results extend and improve the related results in the literature.