## Convergence of Mann’s type iteration method for generalized asymptotically nonexpansive mappings.(English)Zbl 1471.65043

Summary: Let $$C$$ be a nonempty, closed and convex subset of a real Hilbert space $$H$$. Let $$T_{i}: C \to H$$, $$i=1,2,\dots ,N$$ be a finite family of generalized asymptotically nonexpansive mappings. It is our purpose, in this paper to prove strong convergence of Mann’s type method to a common fixed point of $$\{T_{i}:i=1,2,\dots ,N\}$$ provided that the interior of common fixed points is nonempty. No compactness assumption is imposed either on $$T$$ or on $$C$$. As a consequence, it is proved that Mann’s method converges for a fixed point of nonexpansive mapping provided that interior of $$F(T)\neq \emptyset$$. The results obtained in this paper improve most of the results that have been proved for this class of nonlinear mappings.

### MSC:

 65J15 Numerical solutions to equations with nonlinear operators 47H10 Fixed-point theorems 47J25 Iterative procedures involving nonlinear operators
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### References:

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