Implicit midpoint rule for solving quasi inclusion problems in banach spaces

Abstract

The purpose of this paper is by using the generalized forward-backward splitting method to introduce the implicit midpoint rule for solving quasi inclusion problem of accretive operators in Banach spaces. Under certain assumptions, some strong convergence theorems of the sequence generated by the algorithm to a solution of quasi-inclusion problems of accretive operators are proved. Applications to nonlinear variational inclusion problem and convexly constrained linear inverse problem are included. The results presented in the paper extend and improve some recent results announced in the current literatures.