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Mixed approximation for nonexpansive mappings in Banach spaces. (English) Zbl 1195.47045

Summary: A mixed viscosity approximation scheme is proposed for finding fixed points of nonexpansive mappings, and the strong convergence of the scheme to a fixed point of the nonexpansive mapping is proved in a real Banach space with uniformly Gâteaux differentiable norm. A theorem about Halpern type approximation for nonexpansive mappings is also shown.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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References:

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