Viscosity approximation to common fixed points of a nonexpansive semigroup with a generalized contraction mapping. (English) Zbl 1222.47103
Summary: The purpose of this paper is to introduce and construct the implicit and explicit viscosity iterative processes by a generalized contraction mapping \(f\) and a nonexpansive semigroup \( \{T(t):t\geqslant 0\}\), and to prove that, under suitable conditions, these iterative processes converge strongly to a unique common fixed point of \(\{T(t):t\geqslant 0\}\) in reflexive Banach spaces admitting a weakly sequentially continuous duality mapping.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H10 | Fixed-point theorems |
| 47H20 | Semigroups of nonlinear operators |
Keywords:
fixed point; viscosity approximation method; nonexpansive semigroup; strong convergence; Meir-Keeler type mapping; reflexive Banach spaceReferences:
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