Fixed point algorithms for the split problem of demicontractive operators

A fixed point method is introduced for solving the split common fixed point problem of demicontractive operators in Hilbert spaces. By virtue of this fixed point method, we construct an iteration based on Mann’s method for solving the split common fixed point problem of demicontractive operators. Weak convergence analysis is given under some mild assumptions. c ©2017 All rights reserved.

[1]  R. Wittmann Approximation of fixed points of nonexpansive mappings , 1992 .

[2]  Cristina Popirlan,et al.  On the Mann-type iteration and the convex feasibility problem , 2008 .

[3]  Natl Sun Strong convergence and certain control conditions for modified Mann iteration , 2008 .

[4]  Heinz H. Bauschke,et al.  On Projection Algorithms for Solving Convex Feasibility Problems , 1996, SIAM Rev..

[5]  C. Byrne,et al.  A unified treatment of some iterative algorithms in signal processing and image reconstruction , 2003 .

[6]  Abdellatif Moudafi,et al.  The split common fixed-point problem for demicontractive mappings , 2010 .

[7]  Y. Liou,et al.  Regularized Methods for the Split Feasibility Problem , 2012 .

[8]  F. Browder,et al.  Construction of fixed points of nonlinear mappings in Hilbert space , 1967 .

[9]  Jen-Chih Yao,et al.  Split common fixed point problem for two quasi-pseudo-contractive operators and its algorithm construction , 2015 .

[10]  N. Shahzad,et al.  Minimum-norm solution of variational inequality and fixed point problem in banach spaces , 2015 .

[11]  Jen-Chih Yao,et al.  An extragradient method for solving split feasibility and fixed point problems , 2012, Comput. Math. Appl..

[12]  Hong-Kun Xu,et al.  Cyclic algorithms for split feasibility problems in Hilbert spaces , 2011 .

[13]  Y. Liou,et al.  Strong convergence of a self-adaptive method for the split feasibility problem , 2013 .

[14]  Modified semi-implicit midpoint rule for nonexpansive mappings , 2015 .

[15]  Hong-Kun Xu Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces , 2010 .

[16]  Hong-Kun Xu VISCOSITY APPROXIMATION METHODS FOR NONEXPANSIVE MAPPINGS , 2004 .

[17]  Yair Censor,et al.  The Split Common Fixed Point Problem for Directed Operators. , 2010, Journal of convex analysis.

[18]  Shin Min Kang,et al.  Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method , 2010, Comput. Math. Appl..

[19]  Y. Liou,et al.  Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem , 2014 .

[20]  Zhenhua He,et al.  On hybrid split problem and its nonlinear algorithms , 2013 .