Split Common Fixed Point Problem Research Articles

Retracted] The Split Common Fixed Point Problem for Quasi‐Total Asymptotically Nonexpansive Uniformly Lipschitzian Mappings

We introduce an algorithm for solving the split common fixed point problem for quasi‐total asymptotically nonexpansive uniformly Lipschitzian mapping in Hilbert spaces. The results presented in this paper improve and extend some recent corresponding results.

Strong Convergence Theorems for the Generalized Split Common Fixed Point Problem

We introduce the generalized split common fixed point problem (GSCFPP) and show that the GSCFPP for nonexpansive operators is equivalent to the common fixed point problem. Moreover, we introduce a new iterative algorithm for finding a solution of the GSCFPP and obtain some strong convergence theorems under suitable assumptions.

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

We introduce a new iterative algorithm for solving the split common fixed point problem for countable family of nonexpansive operators. Under suitable assumptions, we prove that the iterative algorithm strongly converges to a solution of the problem.

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 fixed‐point 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 improve and extend the corresponding results announced by many others.

Retracted: The Split Common Fixed Point Problem for Quasi‐Total Asymptotically Nonexpansive Uniformly Lipschitzian Mappings

Retracted: The Split Common Fixed Point Problem for Quasi‐Total Asymptotically Nonexpansive Uniformly Lipschitzian Mappings

The Split Common Fixed Point Problem for Total Asymptotically Strictly Pseudocontractive Mappings

The purpose of this paper is to propose an algorithm for solving the split common fixed point problems for total asymptotically strictly pseudocontractive mappings in infinite‐dimensional Hilbert spaces. The results presented in the paper improve and extend some recent results of Moudafi (2011 and 2010), Xu (2010 and 2006), Censor and Segal (2009), Censor et al. (2005), Masad and Reich (2007), Censor et al. (2007), Yang (2004), and others.

Cyclic algorithms for split feasibility problems in Hilbert spaces

The split common fixed point problem (SCFPP) is equivalently converted to a common fixed point problem of a finite family of class- T operators. This enables us to introduce new cyclic algorithms to solve the SCFPP and the multiple-set split feasibility problem.

A note on the split common fixed-point problem for quasi-nonexpansive operators

Based on the very recent work by Censor and Segal (2009) [1], and inspired by Xu (2006) [9], Zhao and Yang (2005) [10], and Bauschke and Combettes (2001) [2], we introduce and analyze an algorithm for solving the split common fixed-point problem for the wide class of quasi-nonexpansive operators in Hilbert spaces. Our results improve and develop previously discussed feasibility problems and related algorithms.

The split common fixed-point problem for demicontractive mappings

Based on the very recent work by Censor and Segal (2009 J. Convex Anal. 16 587–600) and inspired by Xu (2006 Inverse Problems 22 2021–34) and Yang (2004 Inverse Problems 20 1261–6), we investigate an algorithm for solving the split common fixed-point problem for the class of demicontractive operators in a Hilbert space. Our results improve and/or develop previously discussed feasibility problems and related algorithms. It is worth mentioning that the convex feasibility formalism is at the core of the modeling of many inverse problems and has been used to model significant real-world problems, for instance, in sensor networks, in radiation therapy treatment planning, in computerized tomography and data compression, see Censor et al (2006 Phys. Med. Biol. 51 2353–65) and Combettes (1996 Adv. Imaging Electron. Phys. 95 155–270) and references therein.