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Zbl 1142.47329
Petruşel, A.; Yao, J.-C.
Viscosity approximation to common fixed points of families of nonexpansive mappings with generalized contractions mappings. (English)
[J] Nonlinear Anal., Theory Methods Appl. 69, No. 4, A, 1100-1111 (2008). ISSN 0362-546X

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 2000:: *47H09 Mappings defined by "shrinking" properties
65J15 Equations with nonlinear operators (numerical methods)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: common fixed point; sunny and nonexpansive retraction; nonexpansive mapping; Banach space; Meir-Keeler type mapping; $\psi $-contraction

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Zentralblatt MATH Berlin [Germany]