Variational Inclusions Involving Generalized Set-Valued Quasi-Contractive Mappings in Banach Spaces

In this paper, we give a characterization of strong convergence theorem of the Ishikawa iterative sequence with errors for the generalized set-valued variational inclusion problem involving a generalized set-valued quasi-contractive mapping in a real Banach space. First, the existence of the solution of the generalized set-valued variational inclusion problem is proved. Then, using the existence result, the Ishikawa iterative algorithm with errors is constructed and the convergence of the iterative sequences is proved. Finally, numerical experiments are proposed to support the main result. The results improve and extend some known results.