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An approximation method for strictly pseudocontractive mappings

Authors:	Rudong Chen Pei-Kee Lin Yisheng Song

Institution:	1. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China;2. Department of Mathematics, University of Memphis, Memphis, TN 38152, USA;3. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China

Abstract:	Let K $K$ be a closed convex subset of a q $q$ -uniformly smooth separable Banach space, T:K→K $T : K \to K$ a strictly pseudocontractive mapping, and f:K→K $f : K \to K$ an L $L$ -Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1) $t \in (0, 1)$ , let _x_t $x_{t}$ be the unique fixed point of tf+(1-t)T $tf + (1 - t) T$ . We prove that if T $T$ has a fixed point, then {_x_t} ${x_{t}}$ converges to a fixed point of T $T$ as t $t$ approaches to 0.

Keywords:	Strictly pseudocontractive mapping Strongly pseudocontractive mapping Viscosity approximation Fixed point
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