Weak and strong convergence theorems of common fixed points for a pair of nonexpansive and asymptotically nonexpansive mappings
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 44 (2005) no. 1, pp. 83-96 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The purpose of this paper is to establish some weak and strong convergence theorems of modified three-step iteration methods with errors with respect to a pair of nonexpansive and asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper generalize, improve and unify a few results due to Chang [1], Liu and Kang [5], Osilike and Aniagbosor [7], Rhoades [8] and Schu [9], [10] and others. An example is included to demonstrate that our results are sharp.
The purpose of this paper is to establish some weak and strong convergence theorems of modified three-step iteration methods with errors with respect to a pair of nonexpansive and asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper generalize, improve and unify a few results due to Chang [1], Liu and Kang [5], Osilike and Aniagbosor [7], Rhoades [8] and Schu [9], [10] and others. An example is included to demonstrate that our results are sharp.
Classification : 47H05, 47H09, 47H10, 47H15, 47J25
Keywords: nonexpansive mappings; asymptotically nonexpansive mappings; common fixed points; modified three-step iteration methods with errors with respect to a pair of mappings
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Liu, Zeqing; Agarwal, Ravi P.; Feng, Chi; Kang, Shin Min. Weak and strong convergence theorems of common fixed points for a pair of nonexpansive and asymptotically nonexpansive mappings. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 44 (2005) no. 1, pp. 83-96. http://geodesic.mathdoc.fr/item/AUPO_2005_44_1_a8/

[1] Chang S. S.: On the approximation problem of fixed points for asymptotically nonexpansive mappings. Indian J. Pure Appl. Math. 32 (2001), 1297–1307. | Zbl

[2] Chang S. S.: Some problems and results in the study of nonlinear analysis. Nonlinear Anal. TMA 30 (1997), 4197–4208. | Zbl

[3] Goebel K., Kirk W. A.: A fixed point theorem for asymptotically nonexpansive mappings. Proc. Amer. Math. Soc. 35 (1972), 171–174. | Zbl

[4] Gornicki J.: Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces. Comment. Math. Univ. Carolina 30 (1989), 249–252. | Zbl

[5] Liu Z., Kang S. M.: Weak and strong convergence for fixed points of asymptotically nonexpansive mappings. Acta. Math. Sinica 20 (2004), 1009–1018.

[6] Opial Z.: Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Amer. Math. Soc. 73 (1967), 591–597. | Zbl

[7] Osilike M. O., Aniagbosor S. C.: Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings. Math. Comput. Modelling 32 (2000), 1181–1191. | Zbl

[8] Rhoades B. E.: Fixed point iteration for certain nonlinear mappings. J. Math. Anal. Appl. 183 (1994), 118–120.

[9] Schu J.: Iterative construction of fixed points of asymptotically nonexpansive mappings. J. Math. Anal. Appl. 158 (1991), 407–413. | Zbl

[10] Schu J.: Weak and strong convergence of fixed points of asymptotically nonexpansive mappings. Bull. Austral. Math. Soc. 43 (1991), 153–159.

[11] Xu H. K.: Inequalities in Banach spaces with applications. Nonlinear Anal. TMA 16 (1991), 1127–1138. | Zbl