The existence and convergence of best proximity points for generalized proximal contraction mappings

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Publication Details

Author list: Sintunavarat W., Kumam P.

Publisher: SpringerOpen

Publication year: 2014

Journal: Fixed Point Theory and Applications (1687-1820)

Volume number: 2014

Issue number: 1

ISSN: 1687-1820

eISSN: 1687-1812

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84935887418&doi=10.1186%2f1687-1812-2014-228&partnerID=40&md5=62808758d564e11e72f3c7e708e28fb5

Languages: English-Great Britain (EN-GB)

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Abstract

In 2011, Sadiq Basha (Nonlinear Anal. 74:5844-5850, 2011) studied and established best proximity point theorems for proximal contractions of the first and the second kinds which are more general than the fixed point theorems of self-contractions. The purpose of this paper is to extend the notion of proximal contraction mappings of the first and the second kinds. We also establish the existence and convergence of best proximity point theorems for these classes and give an example to validate our main results. MSC: 47H10, 47H09. ฉ 2014, Sintunavarat and Kumam; licensee Springer.

Keywords

proximal contraction mapping of the first kind, proximal contraction mapping of the second kind