Please use this identifier to cite or link to this item: http://cmuir.cmu.ac.th/jspui/handle/6653943832/59747
Title: Edelstein's method and fixed point theorems for some generalized nonexpansive mappings
Authors: S. Dhompongsa
W. Inthakon
A. Kaewkhao
Keywords: Mathematics
Issue Date: 1-Feb-2009
Abstract: A new condition for mappings, called condition (C), which is more general than nonexpansiveness, was recently introduced by Suzuki [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095]. Following the idea of Kirk and Massa Theorem in [W.A. Kirk, S. Massa, Remarks on asymptotic and Chebyshev centers, Houston J. Math. 16 (1990) 364-375], we prove a fixed point theorem for mappings with condition (C) on a Banach space such that its asymptotic center in a bounded closed and convex subset of each bounded sequence is nonempty and compact. This covers a result obtained by Suzuki [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095]. We also present fixed point theorems for this class of mappings defined on weakly compact convex subsets of Banach spaces satisfying property (D). Consequently, we extend the results in [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095] to many other Banach spaces. © 2008 Elsevier Inc. All rights reserved.
URI: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=54149110520&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/59747
ISSN: 10960813
0022247X
Appears in Collections:CMUL: Journal Articles

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