A new class of S -contractions in complete metric spaces and GP -contractions in ordered metric spaces

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Publication Details

Author list: Komal S., Kumam P.

Publisher: SpringerOpen

Publication year: 2016

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

Volume number: 2016

Issue number: 1

ISSN: 1687-1820

eISSN: 1687-1812

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84977107128&doi=10.1186%2fs13663-016-0556-x&partnerID=40&md5=1016481ec5a548ad0d7c69c47d66b18d

Languages: English-Great Britain (EN-GB)

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Abstract

The basic purpose of this article is to define new so-called S-contractions and discuss the presence of common best proximity point theorems for such contractions in the setting of Cauchy metric spaces. We also calculate some common optimal approximate solutions of some fixed point equations when there does not exist any common fixed point. We also introduce the notions of GP-functions and GP-contractions with the help of P-functions and prove the existence of a unique best proximity point in partially order metric spaces. We give some examples that justify the validity of our results. These results extend and unify many existing results in the literature. ฉ 2016, Komal and Kumam.

Keywords

GP-contraction, GP-function, P-property, S-contraction