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- W4234592267 abstract "Let $E$ be a Banach space, $C$ a nonempty closed convex subset of $E$, $f : C to C$ a contraction, and $T_i : C to C$ a nonexpansive mapping with nonempty $F := bigcap_{i = 1}^N Fix(T_i)$, where $N ge 1$ is an integer and $Fix(T_i)$ is the set of fixed points of $T_i$. Let ${x_t^n}$ be the sequence defined by $x_t^n = tf(x_t^n) + (1-t) T_{n+N} T_{n+N-1} cdots T_{n+1} x_t^n$ ($0 lt t lt 1$). First, it is shown that as $t to 0$, the sequence ${x_t^n}$ converges strongly to a solution in $F$ of certain variational inequality provided $E$ is reflexive and has a weakly sequentially continuous duality mapping. Then it is proved that the iterative algorithm $x_{n+1} = lambda_{n+1} f(x_n) + (1-lambda_{n+1}) T_{n+1} x_n$ ($n ge 0$) converges strongly to a solution in $F$ of certain variational inequality in the same Banach space provided the sequence ${lambda_n}$ satisfies certain conditions and the sequence ${x_n}$ is weakly asymptotically regular. Applications to the convex feasibility problem are included." @default.
- W4234592267 created "2022-05-12" @default.
- W4234592267 creator A5085884589 @default.
- W4234592267 date "2007-08-01" @default.
- W4234592267 modified "2023-10-18" @default.
- W4234592267 title "CONVERGENCE THEOREMS OF ITERATIVE ALGORITHMS FOR A FAMILY OF FINITE NONEXPANSIVE MAPPINGS" @default.
- W4234592267 doi "https://doi.org/10.11650/twjm/1500404763" @default.
- W4234592267 hasPublicationYear "2007" @default.
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