Best Proximity Points for Some Classes of Proximal Contractions

Maryam A. Alghamdi, Naseer Shahzad and Francesca Vetro

Abstract and Applied Analysis, 2013, vol. 2013, 1-10

Abstract:

Given a self-mapping and a non-self-mapping , the aim of this work is to provide sufficient conditions for the existence of a unique point , called g -best proximity point, which satisfies . In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function , thereby getting an optimal approximate solution to the equation . 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.

Date: 2013
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2013/713252.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2013/713252.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:713252

DOI: 10.1155/2013/713252

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().