Weak and strong convergence theorems for the split common fixed point problem with demicontractive operators

Abstract

A novel iterative algorithm is introduced for solving the split common fixed point problem with demicontractive operators. Weak and strong convergence of the algorithm is discussed. The step-sizes of the algorithm are chosen in such a way that the implementation of the algorithm does not depend on operator norms. The main results proven in this paper extend and improve some results of Yao et al. [Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem. Fixed Point Theor Appl. 2014;2014:183], Boikanyo [A strongly convergent algorithm for the split common fixed point problem. Appl Math Comput. 2015;265:844–853] and Cui and Wang [Iterative methods for the split common fixed point problem in Hilbert spaces. Fixed Point Theor Appl. 2014;2014:78].