Coupled Fixed Point Theorems with New Implicit Relations and an Application. (11th November 2014)

• Record Type: Journal Article
• Authors: Babu, G. V. R.; Sailaja, P. D.
• Other Names: Neidhardt Hagen Academic Editor.
• Is Part Of: Journal of operators. Volume 2014(2014)
• Publication Date: 2014-11-11
• Subjects: Operator theory -- Periodicals; Operator theory; Periodicals; 515.724
• DOI: 10.1155/2014/389646
• Languages: English
• ISSNs: 2314-5064

Abstract

Abstract : We introduce two new classes of implicit relationsS andS ′ whereS ′ is a proper subset ofS, and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010). We prove the existence of coupled fixed points for the maps satisfying an implicit relation inS . These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relationS ′, whereS ′ ⊂ S . Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010) to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006). As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation.