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Approximating common fixed points of two nonexpansive mappings in Banach spaces

Published online by Cambridge University Press:  17 April 2009

Sachiko Atsushiba  and
Wataru Takahashi
Sachiko Atsushiba
Affiliation:
Department of Mathematical and Computing SciencesTokyo Institute of TechnologyO-okayama, Meguro-kuTokyo 152, Japan e-mail: atsusiba@is.titech.ac.jp, wataru@is.titech.ac.jp
Wataru Takahashi
Affiliation:
Department of Mathematical and Computing SciencesTokyo Institute of TechnologyO-okayama, Meguro-kuTokyo 152, Japan e-mail: atsusiba@is.titech.ac.jp, wataru@is.titech.ac.jp
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Abstract

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Let C be a nonempty closed convex subset of a real Banach space E and let S, T be nonexpansive mappings of C into itself. In this paper, we consider the following iteration procedure of Mann's type for approximating common fixed points of two mappings S and T:

where {αn is a sequence in [0,1]. Using some ideas in the nonlinear ergodic theory, we prove that the iterates converge weakly to a common fixed point of the nonexpansive mappings T and S in a uniformly convex Banach space which satisfies Opial's condition or whose norm is Fréchet differentiable.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 1 , February 1998 , pp. 117 - 127
Copyright
Copyright © Australian Mathematical Society 1998

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