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

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

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.

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Authors and Affiliations

  1. School of Mathematics, The University of Birmingham, The Watson Building, Edgbaston, Birmingham, B15 2TT, UK

    M. Abbas

  2. Department of Mathematics, Lahore University of Management Sciences, 54792, Lahore, Pakistan

    M. Abbas & T. Nazir

  3. Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camí de Vera s/n, 46022, Valencia, Spain

    S. Romaguera

Authors
  1. M. Abbas
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  2. T. Nazir
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  3. S. Romaguera
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Correspondence to M. Abbas.

Additional information

S. Romaguera acknowledges the support of the Ministry of Science and Innovation of Spain, grant MTM2009-12872-C02-01.

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Abbas, M., Nazir, T. & Romaguera, S. Fixed point results for generalized cyclic contraction mappings in partial metric spaces. RACSAM 106, 287–297 (2012). https://doi.org/10.1007/s13398-011-0051-5

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  • DOI: https://doi.org/10.1007/s13398-011-0051-5

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