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Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings
Author
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-06
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
The purpose of this article is to present a general viscosity iteration process {xn} which defined by xn+1=(I-αnA)Txn+βnγf(xn)+(αn-βn)xn and to study the convergence of {xn}, where T is a nonexpansive mapping and A is a strongly positive linear operator, if {αn}, {βn} satisfy appropriate conditions, then iteration sequence {xn} converges strongly to the unique solution x*∈f(T) of variational inequality 〈(A−γf)x*,x−x*〉≥0, for all x∈f(T).
Meanwhile, a approximate iteration algorithm is presented which is used to calculate the fixed point of nonexpansive mapping and solution of variational inequality, the error estimate is also given.
The results presented in this paper extend, generalize, and improve the results of Xu, G.
Marino and Xu and some others.
American Psychological Association (APA)
Su, Yongfu. 2012. Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-484479
Modern Language Association (MLA)
Su, Yongfu. Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings. Abstract and Applied Analysis No. 2012 (2012), pp.1-18.
https://search.emarefa.net/detail/BIM-484479
American Medical Association (AMA)
Su, Yongfu. Approximate Iteration Algorithm with Error Estimate for Fixed Point of Nonexpansive Mappings. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-18.
https://search.emarefa.net/detail/BIM-484479
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-484479