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Best Proximity Points for Some Classes of Proximal Contractions
Joint Authors
Vetro, Francesca
Shahzad, Naseer
Alghamdi, Maryam A.
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-09-29
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Given a self-mapping g:A→A and a non-self-mapping T:A→B, the aim of this work is to provide sufficient conditions for the existence of a unique point x∈A, called g-best proximity point, which satisfies dgx,Tx=dA,B.
In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function x→dgx,Tx, thereby getting an optimal approximate solution to the equation Tx=gx.
An iterative algorithm is also presented to compute a solution of such problems.
Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-self-mappings.
American Psychological Association (APA)
Alghamdi, Maryam A.& Shahzad, Naseer& Vetro, Francesca. 2013. Best Proximity Points for Some Classes of Proximal Contractions. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-492608
Modern Language Association (MLA)
Alghamdi, Maryam A.…[et al.]. Best Proximity Points for Some Classes of Proximal Contractions. Abstract and Applied Analysis No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-492608
American Medical Association (AMA)
Alghamdi, Maryam A.& Shahzad, Naseer& Vetro, Francesca. Best Proximity Points for Some Classes of Proximal Contractions. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-492608
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-492608