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Fixed point results for generalized cyclic contraction mappings in partial metric spaces

  • M. Abbas
  • T. Nazir
  • S. Romaguera
Original Paper

Abstract

Rus (Approx. Convexity 3:171–178, 2005) introduced the concept of cyclic contraction mapping. Păcurar and Rus (Nonlinear Anal. 72:1181–1187, 2010) proved some fixed point results for cyclic \({\phi }\)-contraction mappings on a metric space. Karapinar (Appl. Math. Lett. 24:822–825, 2011) obtained a unique fixed point of cyclic weak \({\phi }\)- contraction mappings and studied well-posedness problem for such mappings. On the other hand, Matthews (Ann. New York Acad. Sci. 728:183–197, 1994) introduced the concept of a partial metric as a part of the study of denotational semantics of dataflow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In this paper, we initiate the study of fixed points of generalized cyclic contraction in the framework of partial metric spaces. We also present some examples to validate our results.

Keywords

Partial metric space Fixed point Cyclic contraction 

Mathematics Subject Classification (2000)

47H10 54H25 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of MathematicsThe University of BirminghamBirminghamUK
  2. 2.Department of MathematicsLahore University of Management SciencesLahorePakistan
  3. 3.Instituto Universitario de Matemática Pura y AplicadaUniversitat Politècnica de ValènciaValenciaSpain

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