## Existence and convergence for fixed points of mappings of asymptotically nonexpansive type.(English)Zbl 0747.47041

This article deals with mappings $$T:C\to C$$ of asymptotically nonexpansive type of a nonempty closed convex subset in a uniformly convex Banach space $$X$$ or, in other words, with mappings for which $\varlimsup_{n\to\infty}\sup_{y\in C}(\| T^ nx-T^ ny\|- \| x-y\|)\leq 0.$ The main result is a fixed point theorem for such mappings and a theorem on the weak convergence of the Picard approximations to a fixed point.
Reviewer: P.Zabreiko (Minsk)

### MSC:

 47H10 Fixed-point theorems 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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