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Approximation methods for common fixed points of mean nonexpansive mapping in Banach spaces. (English) Zbl 1203.47045

Summary: Let \(X\) be a uniformly convex Banach space, and let \(S, T\) be a pair of mean nonexpansive mappings. In this paper, it is proved that the sequence of Ishikawa iterations associated with \(S\) and \(T\) converges to a common fixed point of \(S\) and \(T\).

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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References:

[1] Bose, SC, Common fixed points of mappings in a uniformly convex Banach space, Journal of the London Mathematical Society, 18, 151-156, (1978) · Zbl 0404.47030 · doi:10.1112/jlms/s2-18.1.151
[2] Rashwan, RA; Saddeek, AM, On the Ishikawa iteration process in Hilbert spaces, Collectanea Mathematica, 45, 45-52, (1994) · Zbl 0817.47074
[3] Berinde, V, On the convergence of the Ishikawa iteration in the class of quasi contractive operators, Acta Mathematica Universitatis Comenianae, 73, 119-126, (2004) · Zbl 1100.47054
[4] Maingé, P-E, Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces, Journal of Mathematical Analysis and Applications, 325, 469-479, (2007) · Zbl 1111.47058 · doi:10.1016/j.jmaa.2005.12.066
[5] Rashwan, RA, On the convergence of Mann iterates to a common fixed point for a pair of mappings, Demonstratio Mathematica, 23, 709-712, (1990) · Zbl 0731.47053
[6] Song, Y; Chen, R, Iterative approximation to common fixed points of nonexpansive mapping sequences in reflexive Banach spaces, Nonlinear Analysis: Theory, Methods & Applications, 66, 591-603, (2007) · Zbl 1114.47055 · doi:10.1016/j.na.2005.12.004
[7] Ćirić, LjB; Ume, JS; Khan, MS, On the convergence of the Ishikawa iterates to a common fixed point of two mappings, Archivum Mathematicum, 39, 123-127, (2003) · Zbl 1109.47312
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