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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.

47H09Mappings defined by “shrinking” properties
65J15Equations with nonlinear operators (numerical methods)
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
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