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Viscosity approximation to common fixed points of families of nonexpansive mappings with generalized contractions mappings. (English) Zbl 1142.47329

Summary: Let \(X\) be a reflexive and smooth real Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation scheme \(x_{n+1}=\lambda _{n+1}f(x_n)+(1 - \lambda _{n+1})T_{n+1}x_n\) (where \(f\) is a generalized contraction mapping) for infinitely many nonexpansive self-mappings \(T_{1},T_{2},T_{3},\dots \) in \(X\). We establish a strong convergence result which generalizes some results in the literature.

MSC:

47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
65J15 Numerical solutions to equations with nonlinear operators
47H10 Fixed-point theorems
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