Split common fixed point problem for two quasi-pseudo-contractive operators and its algorithm construction

Common fixed points of quasi-contractive operators

We establish a general theorem to approximate common fixed points of quasi-contractive operators on a normed space through the modified Ishikawa iteration process with errors in the sense of Liu [8]. Our result generalizes and improves upon, among others, the corresponding result of Berinde [1]. 2000 Mathematical Subject Clasification: Primary 47H10, 47H17: Secondary 54H25

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. ...

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

On the Strong Convergence of an Algorithm about Firmly Pseudo-Demicontractive Mappings for the Split Common Fixed-Point Problem

Based on the recent work by Censor and Segal 2009 J. Convex Anal.16 , and inspired by Moudafi 2010 Inverse Problems 26 , we modify the algorithm of demicontractive operators proposed by Moudafi and study the modified algorithm for the class of firmly pseudodemicontractive operators to solve the split common fixed-point problem in a Hilbert space. We also give the strong convergence theorem unde...

Implicit Mann fixed point iterations for pseudo-contractive mappings

Let K be a compact convex subset of a real Hilbert space H and T:K→K a continuous hemicontractive map. Let {an},{bn} and {cn} be real sequences in [0, 1] such that an+bn+cn=1, and {un} and {vn} be sequences in K. In this paper we prove that, if {bn}, {cn} and {vn} satisfy some appropriate conditions, then for arbitrary x0K, the sequence {xn} defined iteratively by xn=anxn−1+bnTvn+cnun;n≥1, conv...