Volume 10, Issue 8, pp 4143--4149
Publication Date: 2017-08-10
Yunpeng Zhang - College of Electric Power, North China University of Water Resources and Electric Power, Zhengzhou 450011, China.
Sun Young Cho - Center for General Education, China Medical University, Taichung 40402, Taiwan.
In this paper, a Halpern-like iterative algorithm is investigated for finding a solution of a split feasibility problem and a solution to a nonexpansive operator equation. Strong convergence theorems are established in the framework of infinite dimensional Hilbert spaces.
Convergence analysis, Hilbert space, monotone mapping, split feasibility problem.
 B. A. Bin Dehaish, A. Latif, H. O. Bakodah, X. Qin, A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces, J. Inequal. Appl., 2015 (2015), 14 pages.
 B. A. Bin Dehaish, X. Qin, A. Latif, H. Bakodah, Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321–1336.
 F. E. Browder, Fixed-point theorems for noncompact mappings in Hilbert space, Proc. Natl. Acad. Sci. U.S.A., 53 (1965), 1272–1276.
 C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Probl., 20 (2004), 103–120.
 Y. Censor, T. Bortfeld, B. Martin, A. Trofimov, A unified approach for inversion problems in intensity modulated radiation therapy, Phys. Med. Biol., 51 (2006), 2353–2365.
 Y. Censor, T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, 8 (1994), 221–239.
 Y. Censor, T. Elfving, N. Kopf, T. Bortfeld, The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Probl., 21 (2005), 2071–2084.
 S. Y. Cho, B. A. Bin Dehaish, X. Qin, Weak convergence of a splitting algorithm in Hilbert spaces, J. Appl. Anal. Comput., 7 (2017), 427–438.
 S. Y. Cho, S. M. Kang, Approximation of common solutions of variational inequalities via strict pseudocontractions, Acta Math. Sci. Ser. B Engl. Ed., 32 (2012), 1607–1618.
 S. Y. Cho, W. Li, S. M. Kang, Convergence analysis of an iterative algorithm for monotone operators, J. Inequal. Appl., 2013 (2013), 14 pages.
 N. Fang, Y. Gong, Viscosity iterative methods for split variational inclusion problems and fixed poit problems of a nonexpansive mappings, Commun. Optim. Theory, 2016 (2016), 15 pages.
 L. S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl., 194 (1995), 114–125.
 X. Qin, S. S. Chang, Y. J. Cho, Iterative methods for generalized equilibrium problems and fixed point problems with applications, Nonlinear Anal. Real World App., 11 (2010), 2963–2972.
 X. Qin, S. Y. Cho, Convergence analysis of a monotone projection algorithm in reflexive banach spaces, Acta Math. Sci. Ser. B Engl. Ed., 37 (2017), 488–502.
 X. Qin, J. C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016), 9 pages.
 W. Takahahsi, Weak and strong convergence theorems for families of nonlinear and nonself mappings in Hilbert spaces, J. Nonlinear Var. Anal., 1 (2017), 1–23.
 J. Tang, S. S. Chang, Strong convergence theorem of two-step iterative algorithm for split feasibility problems, J. Inequal. Appl., 2014 (2014), 13 pages.
 J. Tang, S. S. Chang, J. Dong, Split equality fixed point problems for two quasi-asymptotically pseudocontractive mappings, J. Nonlinear Funct. Anal., 2017 (2017), 15 pages.
 H. Y. Zhou, Y.Wang, Adaptively relaxed algorithms for solving the split feasibility problem with a new step size, J. Inequal. Appl., 2014 (2014), 22 pages.