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Wen, Meng; Hu, Changsong; Wu, Zhiyu

Convergence of implicit and explicit schemes for an asymptotically nonexpansive mapping in \(q\)-uniformly smooth and strictly convex Banach spaces. (English) Zbl 1325.47134

J. Appl. Math. 2012, Article ID 474031, 15 p. (2012).
Summary: We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in \(q\)-uniformly smooth and strictly convex Banach spaces. We also prove strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others.

MSC:

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

Keywords:

Meir-Keeler contractions; strong convergence; implicit schemes
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\textit{M. Wen} et al., J. Appl. Math. 2012, Article ID 474031, 15 p. (2012; Zbl 1325.47134)
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References:

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