New algorithms designed for the split common fixed point problem of quasi-pseudocontractions

Multidirectional hybrid algorithm for the split common fixed point problem and application to the split common null point problem

In this article, a new multidirectional monotone hybrid iteration algorithm for finding a solution to the split common fixed point problem is presented for two countable families of quasi-nonexpansive mappings in Banach spaces. Strong convergence theorems are proved. The application of the result is to consider the split common null point problem of maximal monotone operators in Banach spaces. ...

A New Iterative Method for the Split Common Fixed Point Problem in Hilbert Spaces

The split common fixed-point problem is an inverse problem that consists in finding an element in a fixed-point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper, we propose a new algorithm that is completely different from the existing algorithms. Under standard assumptions, we establish a weak convergence theorem of the proposed algorith...

Strong Convergence of the Viscosity Approximation Process for the Split Common Fixed-Point Problem of Quasi-Nonexpansive Mappings

Very recently, Moudafi 2011 introduced an algorithm with weak convergence for the split common fixed-point problem. In this paper, we will continue to consider the split common fixedpoint problem. We discuss the strong convergence of the viscosity approximation method for solving the split common fixed-point problem for the class of quasi-nonexpansive mappings in Hilbert spaces. Our results imp...

Strong Convergence Theorems for the Split Common Fixed Point Problem for Countable Family of Nonexpansive Operators

Strong and Weak Convergence Theorems for Split Common Fixed Problem of Asymptotically Quasi-nonexpansive Mappings

An iterative algorithm is introduced to solve the split common fixed point problems for asymptotically quasi-nonexpansive mappings in Hilbert spaces. The strong and weak convergence of the presented algorithm to some split common fixed point are obtained. The results presented in this paper improve and extend some recent results of Moudafi [Nonlinear Anal. 74 (2011), 4083-4087], Xu [Inverse Pro...