## Strong convergence theorems for nonexpansive nonself-mappings.(English)Zbl 0826.47038

Let $$C$$ be a closed convex subset of a Banach space $$X$$, $$u\in C$$, and $$T: C\to X$$ a nonexpansive map. Then the operator $$S_t$$ defined for $$0< t< 1$$ by $$S_t x= tTx+ (1- t)u$$ is a contraction, and hence has a unique fixed point $$x_t\in C$$ if $$T(C)\subseteq C$$. In this paper the authors discuss various conditions under which $$x_t$$ converges to a fixed point of $$T$$ as $$t\to 1$$.

### MSC:

 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems
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### References:

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