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Keywords:
nonexpansive mappings; asymptotically nonexpansive mappings; common fixed points; modified three-step iteration methods with errors with respect to a pair of mappings
nonexpansive mappings; asymptotically nonexpansive mappings; common fixed points; modified three-step iteration methods with errors with respect to a pair of mappings
Summary:
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.
References:
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[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 0971.47038
[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 0734.47036
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