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Weak convergence theorems for a countable family of strict pseudocontractions in Banach spaces. (English) Zbl 1206.47070

Summary: We investigate the convergence of a Mann-type iterative scheme for a countable family of strict pseudocontractions in a uniformly convex Banach space with Fréchet differentiable norm. We also point out that the condition given by C.E.Chidume and N.Shahzad [Nonlinear Anal., Theory Methods Appl., Ser.A, Theory Methods 72, No. 3–4, A, 1257–1265 (2010; Zbl 1193.47065)] is not satisfied in a real Hilbert space. We show that their results are still true under a new condition.

MSC:

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

Citations:

Zbl 1193.47065
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References:

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