## 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
Full Text: