Skip to main content
SpringerLink
Log in

Partial b-Metric Spaces and Fixed Point Theorems

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

The purpose of this paper is to introduce the concept of partial b-metric spaces as a generalization of partial metric and b-metric spaces. An analog to Banach contraction principle, as well as a Kannan type fixed point result is proved in such spaces. Some examples are given which illustrate the results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aghajani, A., Abbas, M., Roshan, J.R.: Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces. To appear in Mathematica Slovaka (2013)

  2. Bakhtin I.A.: The contraction mapping principle in quasimetric spaces. Funct. Anal. Unianowsk Gos. Ped. Inst. 30, 26–37 (1989)

    MATH  MathSciNet  Google Scholar 

  3. Khamski M.A., Hussain N.: KKM mappings in metric type spaces. Nonlinear Anal. 73(9), 3123–3129 (2010)

    Article  MathSciNet  Google Scholar 

  4. Boriceanu, M., Bota, M., Petrusel, A.: Mutivalued fractals in b-metric spaces. Cen. Eur. J. Math 8(2), 367–377 (2010)

    Google Scholar 

  5. Bota M., Molnar A., Csaba V.: On Ekeland’s variational principle in b-metric spaces. Fixed Point Theory 12, 21–28 (2011)

    MATH  MathSciNet  Google Scholar 

  6. Jovanović, M., Kadelburg, Z., Radenović, S.: Common fixed point results in metric type spaces. Fixed Point Theory Appl. 2010 (Article ID 978121) (2010). doi:10.1155/2010/978121

  7. Heckmann R.: Approximation of metric spaces by partial metric spaces. Appl. Categ. Struct. 7, 71–83 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kannan R.: Some results on fixed points. Am. Math. Monthly 76, 405–408 (1969)

    Article  MATH  Google Scholar 

  9. Czerwik S.: Contraction mappings in b-metric spaces. Acta Mathematica et Informatica Universitatis Ostraviensis 1, 5–11 (1993)

    MATH  MathSciNet  Google Scholar 

  10. Czerwik S.: Nonlinear set-valued contraction mappings in b-metric spaces. Atti Sem. Mat. Univ. Modena 46, 263–276 (1998)

    MATH  MathSciNet  Google Scholar 

  11. Matthews, S.G.: Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Application. Ann. New York Acad. Sci. 728, 183–197 (1994)

  12. O’Neill, S.J.: Partial metrics, valuations and domain theory, in: Proc. 11th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci. 806, 304-315 (1996)

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Shri Vaishnav Institute of Technology and Science, Gram Baroli, Sanwer Road, Indore, MP, 453331, India

    Satish Shukla

Authors
  1. Satish Shukla
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Satish Shukla.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shukla, S. Partial b-Metric Spaces and Fixed Point Theorems. Mediterr. J. Math. 11, 703–711 (2014). https://doi.org/10.1007/s00009-013-0327-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00009-013-0327-4

Mathematics Subject Classification (2000)

Keywords

Search

Navigation