Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation. (20th June 2013)

• Record Type: Journal Article
• Authors: Chauhan, Sunny; Imdad, Mohammad; Vetro, Calogero
• Other Names: Kong Lingju Academic Editor.
• Is Part Of: Journal of operators. Volume 2013(2013)
• Publication Date: 2013-06-20
• Subjects: Operator theory -- Periodicals; Operator theory; Periodicals; 515.724
• DOI: 10.1155/2013/186910
• Languages: English
• ISSNs: 2314-5064

Abstract

Abstract : We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.