A Note on the General Split Common Fixed Point Problem in Hilbert Spaces

Abstract

This paper examines a general form of the split common fixed point problem in which a finite family of bounded linear operators is involved. We propose viscosity approximation methods with choosing two different types of stepsizes (one depends on operator norms and the other is selected in a self-adaptive way) for classes of attracting quasi-nonexpansive mappings and demicontractive mappings, respectively. Using the Landweber technique and some properties of the attracting quasi-nonexpansiveness, strong convergence results of the proposed methods are established in Hilbert spaces. Our results presented in this paper generalize many existing results in the literature.