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Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Convex Metric Spaces
Joint Authors
Phuengrattana, Withun
Suantai, Suthep
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-09-18
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
We introduce a new modified Halpern iteration for a countable infinite family of nonexpansive mappings {Tn} in convex metric spaces.
We prove that the sequence {xn} generated by the proposed iteration is an approximating fixed point sequence of a nonexpansive mapping when {Tn} satisfies the AKTT-condition, and strong convergence theorems of the proposed iteration to a common fixed point of a countable infinite family of nonexpansive mappings in CAT(0) spaces are established under AKTT-condition and the SZ-condition.
We also generalize the concept of W-mapping for a countable infinite family of nonexpansive mappings from a Banach space setting to a convex metric space and give some properties concerning the common fixed point set of this family in convex metric spaces.
Moreover, by using the concept of W-mappings, we give an example of a sequence of nonexpansive mappings defined on a convex metric space which satisfies the AKTT-condition.
Our results generalize and refine many known results in the current literature.
American Psychological Association (APA)
Phuengrattana, Withun& Suantai, Suthep. 2011. Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Convex Metric Spaces. Abstract and Applied Analysis،Vol. 2011, no. 2011, pp.1-18.
https://search.emarefa.net/detail/BIM-508946
Modern Language Association (MLA)
Phuengrattana, Withun& Suantai, Suthep. Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Convex Metric Spaces. Abstract and Applied Analysis No. 2011 (2011), pp.1-18.
https://search.emarefa.net/detail/BIM-508946
American Medical Association (AMA)
Phuengrattana, Withun& Suantai, Suthep. Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Convex Metric Spaces. Abstract and Applied Analysis. 2011. Vol. 2011, no. 2011, pp.1-18.
https://search.emarefa.net/detail/BIM-508946
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-508946