The Split Common Fixed Point Problem of two Infinite Families of Demicontractive Mappings and the Split Common Null Point Problem

Abstract

In this paper, we introduce a new algorithm based on viscosity iteration method for solving the split common fixed point problem for $k$-demicontractive mappings  and the split common null point problem and the split equilibrium problem. As application, we obtain strong convergence theorems for   split monotone variational inclusion and split variational inequality problems. Our results improve and extend the results of Cui and Wang, Takahashi, Tang and Lui, Moudafi, as well as
Eslamian and Vahidi.