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Title: | Edelstein's method and fixed point theorems for some generalized nonexpansive mappings |
Authors: | S. Dhompongsa W. Inthakon A. Kaewkhao |
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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