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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 ${x}_{n+1}={\lambda }_{n+1}f\left({x}_{n}\right)+\left(1-{\lambda }_{n+1}\right){T}_{n+1}{x}_{n}$ (where $f$ is a generalized contraction mapping) for infinitely many nonexpansive self-mappings ${T}_{1},{T}_{2},{T}_{3},\cdots$ in $X$. We establish a strong convergence result which generalizes some results in the literature.
##### MSC:
 47H09 Mappings defined by “shrinking” properties 65J15 Equations with nonlinear operators (numerical methods) 47H10 Fixed point theorems for nonlinear operators on topological linear spaces