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Approximation of fixed points of asymptotically pseudocontractive mappings in Banach spaces. (English) Zbl 1049.47057

Authors’ abstract: “Let \(T\) be an asymptotically pseudocontractive self-mapping of a nonempty closed convex subset \(D\) of a reflexive Banach space \(X\) with a Gâteaux differentiable norm. We deal with the problem of strong convergence of almost fixed points \(x_n=\mu_n T^n x_n+(1-\mu_n)u\) to a fixed point of \(T\). Next, this result is applied to deal with the strong convergence of the explicit iteration process \(z_{n+1}(\alpha_n T^n z_n+ (1-\alpha_n)z_n)+ (1-v_{n+1})u\) to a fixed point of \(T\).”

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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