The viscosity approximation forward-backward splitting method for the implicit midpoint rule of quasi inclusion problems in Banach spaces

The purpose of this paper is to introduce a viscosity approximation forward-backward splitting method for the implicit midpoint rule of an accretive operators and m-accretive operators in Banach spaces. The strong convergence of this viscosity method is proved under certain assumptions imposed on the sequence of parameters. The results presented in the paper extend and improve some recent results announced in the current literature. Moreover, some applications to the minimization optimization problem and the linear inverse problem are presented. (C) 2017 All rights reserved.