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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 $t\to 1$.

47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
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