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COMMON FIXED POINTS OF A PAIR OF NON-EXPANSIVE MAPPINGS WITH APPLICATIONS TO CONVEX FEASIBILITY PROBLEMS

Published online by Cambridge University Press:  25 November 2009

XIAOLONG QIN ,
SUN YOUNG CHO  and
HAIYUN ZHOU
XIAOLONG QIN*
Affiliation:
Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea e-mails: qxlxajh@163.com, ooly61@yahoo.co.kr
SUN YOUNG CHO
Affiliation:
Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea e-mails: qxlxajh@163.com, ooly61@yahoo.co.kr
HAIYUN ZHOU
Affiliation:
Department of Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China e-mail: witman66@yahoo.com.cn
*
*Corresponding author.
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Abstract

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Let C be a non-empty closed convex subset of a reflexive and strictly convex Banach space E which also has a weakly continuous duality map Jφ(x) with the gauge φ. Let S and T be non-expansive mappings from C into itself such that F = F(S) ∩ F(T) ≠ ∅. Let {αn} and {βn} be sequences in (0, 1). Let {xn} be a sequence defined by where u ∈ C is a given point. Assume that the following restrictions imposed on the control sequences are satisfied:

Then the sequence {xn} converges strongly to x* ∈ F, where x* = Q(u) and Q: C → F is the unique sunny non-expansive retraction from C onto F.

Keywords

47H0947H1047J25
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 2 , May 2010 , pp. 241 - 252
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

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