FURTHER INVESTIGATION INTO APPROXIMATION OF A COMMON SOLUTION OF FIXED POINT PROBLEMS AND SPLIT FEASIBILITY PROBLEMS 被引量：1

FURTHER INVESTIGATION INTO APPROXIMATION OF A COMMON SOLUTION OF FIXED POINT PROBLEMS AND SPLIT FEASIBILITY PROBLEMS

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摘要 The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann＇s iterative method and the Halpern＇s approximation method, we propose an iterative algorithm for finding an element of the set F（T）∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature. The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann＇s iterative method and the Halpern＇s approximation method, we propose an iterative algorithm for finding an element of the set F（T）∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.

作者 Y.SHEHU O.T.MEWOMO F.U.OGBUISI

机构地区 Department of Mathematics School of Mathematics

出处《Acta Mathematica Scientia》 SCIE CSCD 2016年第3期913-930,共18页 数学物理学报（B辑英文版）

关键词 strong convergence split feasibility problem uniformly convex uniformly smooth fixed point problem right Bregman strongly nonexpansive mappings strong convergence split feasibility problem uniformly convex uniformly smooth fixed point problem right Bregman strongly nonexpansive mappings

分类号 O177.91 [理学—基础数学] O562.1 [理学—原子与分子物理]

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1Alber Y I. Metric and generalized projection operator in Banach spaces: properties and applica- tions//Theory and Applications of Nonlinear Operators of Accretive and Monotone Type. Vol 178 of Lecture Notes in Pure and Applied Mathematics. New York: Dekker, 1996:15- 50.
2Byrne C. Iterative oblique projection onto convex sets and the split feasibility problem. Inverse Problems, 2002, 18(2): 441-453.
3Censor Y, Bortfeld T, Martin B, Trofimov A. A unified approach for inversion problem in intensity- modulated radiation therapy. Phy Med Biol, 2006, 51:2353-2365.
4Censor Y, Elfving T, Kopf N, Bortfeld T. The multiple-sets split feasibility problem and its applications for inverse problems. Inverse Problems 2005, 21(6): 2071-2084.
5Censor Y, Elfving T. A multiprojection algorithm using Bregman projections in a product space. Numerical Algorithms, 1994, 8(2-4): 221-239.
6Censor Y, Lent A. An iterative row-action method for interval convex programming. J Optim Theory Appl, 1981, 34:321-353.
7Censor Y, Motova A, Segal A. Perturbed projections and subgradient projections for the multiple-sets split feasibility problem. J Math Anal Appl, 2007, 327(2): 1244-1256.
8Censor Y, Segal A. The split common fixed point problem for directed operators. J Convex Anal, 2009, 16(2): 587-600.
9Cioranescu I. Geometry of Banaeh Spaces, Duality Mappings and Nonlinear Problems. Dordrecht: Kluwer, 1990.
10Dunford N, Schwartz J T. Linear Operators I. New York: Wiley Interscience, 1958.