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Strong convergence theorems for a countable family of Lipschitzian mappings. (English) Zbl 1202.47081

Summary: We modify the iterative method introduced by T.-H.Kim and H.-K.Xu [Nonlinear Anal., Theory Methods Appl.64, No.5 (A), 1140–1152 (2006; Zbl 1090.47059)] for a countable family of Lipschitzian mappings by the hybrid method of W.Takahashi, Y.Takeuchi and R.Kubota [J. Math.Anal.Appl.341, No.1, 276–286 (2008; Zbl 1134.47052)]. Our results include recent ones concerning asymptotically nonexpansive mappings due to S.Plubtieng and K.Ungchittrakool [Nonlinear Anal.67, No.7 (A), 2306–2315 (2007; Zbl 1133.47051)] and H.Zegeye and N.Shahzad [Nonlinear Anal., Theory Methods Appl.69, No.12, A, 4496–4503 (2008; Zbl 1168.47056); corrigendum ibid.73, No.6, 1905–1907 (2010)] as special cases.

MSC:

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

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