Strong convergence theorems for two relatively nonexpansive mappings in a Banach space

doi:10.3969/j.issn.1000-1565.2012.02.002

Abstract

CLC Number:

O177.91

LIU Ying,CHEN Yong-li. Strong convergence theorems for two relatively nonexpansive mappings in a Banach space[J]. Journal of Hebei University (Natural Science Edition), 2012, 32(2): 118-123.

[1] 张丽娟, 陈俊敏, ZHANG Li-juan, CHEN Jun-min. 有关非扩张映射的带误差的迭代收敛定理 [J]. 河北大学学报（自然科学版） 2007.doi:10.3969/j.issn.1000-1565.2007.03.005
[2] Matsushita SY, Takahashi W. A strong convergence theorem for relatively nonexpansive mappings in a Banach space [J]. Journal of Approximation Theory 2005, 2(2).
[3] BUTNARIU D, REICH S, ZASLAVSKI A J. Asymptotic behavior of relatively nonexpansive operators in Banach spaces [J]. Journal of Applied Analysis 2001, 7.
[4] Dan Butnariu, Simeon Reich, Alexander J. Zaslavski. Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces [J]. Numerical Functional Analysis and Optimization 2003, 5/6(5/6).
[5] CENSOR Y, REICH S. Iterations of paracontractions and firmly nonexpansive operators with applications to feasibility and optimization [J]. Optimization 1996, 37.
[6] HALPERN B. Fixed points of nonexpanding maps [J]. Bulletin of the American Mathematical Society 1967, 73.
[7] ISHIKAWA S. Fixed points by a new iteration method [J]. Proceedings of the American Mathematical Society 1974, 44.
[8] WITTMANN R. Approximation of fixed points of nonexpansive mappings [J]. Archiv der Mathematik 1992, 58.
[9] ALBER Y I, REICH S. An iterative method for solving a class of nonlinear operator equations in Banach spaces [J]. Pan-American Mathematical Journal 1994, 4.
[10] SHIOJI N, TAKAHASHI W. Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces [J]. Proceedings of the American Mathematical Society 1997, 125.
[11] Hong-Kun Xu. Iterative algorithms for nonlinear operators [J]. The Journal of the London Mathematical Society 2002, 1(1).
[12] Martinez-Yanes C, Xu HK. Strong convergence of the CQ method for fixed point iteration processes [J]. Nonlinear Analysis: An International Multidisciplinary Journal 2006, 11(11).
[13] Qin XL, Su YF. Strong convergence theorems for relatively nonexpansive mappings in a Banach space [J]. Nonlinear Analysis: An International Multidisciplinary Journal 2007, 6(6).
[14] Kamimura SJ., Takahashi W.. Strong convergence of a proximal-type algorithm in a Banach space [J]. SIAM Journal on Optimization: A Publication of the Society for Industrial and Applied Mathematics 2003, 3(3).
[15] XU Hongkun. Inequalities in Banach spaces with applications [J]. Nonlinear Analysis-Theory Methods and Applications 1991, 16.
[16] Chidume CE., Khumalo M., Zegeye H.. Generalized projection and approximation of fixed points of nonself maps [J]. Journal of Approximation Theory 2003, 2(2).

Strong convergence theorems for two relatively nonexpansive mappings in a Banach space

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