Skip to main content
SpringerLink
Log in

Fixed point theorems in orbitally \(0\)-complete partial metric spaces via rational contractive conditions

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

We prove a fixed point result in orbitally \(0\)-complete partial metric spaces, using a variant of almost contractive condition that involves a rational expression. Also, a common fixed point result in \(0\)-complete partial metric spaces is obtained. Several consequences are deduced and examples are presented, showing that the given result can be used for proving the existence of (common) fixed points when some known results fail.

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. Abdeljawad, T., Karapinar, E., Taş, K.: Existence and uniqueness of a common fixed point on partial metric spaces. Appl. Math. Lett. 24, 1900–1904 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  2. Abdeljawad, T., Aydi, H., Karapinar, E.: Coupled fixed points for Meir-Keeler contractions in ordered partial metric spaces. Math. Prob. Eng. (2012)

  3. Aydi, H., Karapinar, E.: New Meir–Keeler type tripled fixed point theorems on ordered partial metric spaces. Math. Prob. Eng. (2012)

  4. Aydi, H., Karapinar, E.: A Meir–Keeler common type fixed point theorem on partial metric spaces. Fixed Point Theory Appl. 2012, 26 (2012)

    Article  Google Scholar 

  5. Aydi, H., Hadj-Amor, S., Karapinar, E.: Berinde type generalized contractions on partial metric spaces. Abstr. Appl. Anal. (2013)

  6. Babu, G.V.R., Sandhya, M.L., Kamesvari, M.V.R.: A note on a fixed point theorem of Berinde on weak contractions. Carpathian J. Math. 24, 8–12 (2008)

    MATH  MathSciNet  Google Scholar 

  7. Berinde, V.: General constructive fixed point theorems for Ćirić-type almost contractions in metric spaces. Carpathian J. Math. 24, 10–19 (2008)

    MATH  MathSciNet  Google Scholar 

  8. Browder, F.E., Petryshyn, W.V.: Construction of fixed points of nonlinear mappings in Hilbert spaces. J. Math. Anal. Appl. 20, 197–228 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  9. Bukatin, M., Kopperman, R., Matthews, S., Pajoohesh, H.: Partial metric spaces. Am. Math. Monthly 116, 708–718 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ćirić, Lj.B.: A generalization of Banach’s contraction principle. Proc. Am. Math. Soc. 45, 267–273 (1974)

  11. Dass, B.K., Gupta, S.: An extension of Banach contraction principle through rational expression. Indian J. Pure Appl. Math. 6, 1455–1458 (1975)

    MATH  MathSciNet  Google Scholar 

  12. Ding, H.S., Kadelburg, Z., Nashine, H.K.: Common fixed point theorems for weakly increasing mappings on ordered orbitally complete metric spaces. Fixed Point Theory Appl. 2012, 85 (2012)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  14. Jaggi, D.S.: Some unique fixed point theorems. Indian J. Pure Appl. Math. 8, 223–230 (1977)

    MathSciNet  Google Scholar 

  15. Jleli, M., Karapinar, E., Samet, B.: Further remarks on fixed point theorems in the context of partial metric spaces. Abstr. Appl, Anal (2013)

    Google Scholar 

  16. Karapinar, E.: A note on common fixed point theorems in partial metric spaces. Miskolc Math. Notes 12(2), 185–191 (2011)

    MATH  MathSciNet  Google Scholar 

  17. Karapinar, E., Erhan, I.M.: Fixed point theorems for operators on partial metric spaces. Appl. Math. Lett. 24, 1894–1899 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  18. Karapinar, E., Yuce, I.S.: Fixed point theory for cyclic generalized weak \(\phi \)-contraction on partial metric spaces. Abstr. Appl, Anal (2012)

    Google Scholar 

  19. Karapinar, E., Rakocevic, V.: On cyclic generalized weakly \(C\)-contractions on partial metric spaces. Abstr. Appl, Anal (2013)

    Google Scholar 

  20. Karapinar, E., Shobkolaei, N., Sedghi, S., Vaezpour, S.M.: A common fixed point theorem for cyclic operators on partial metric spaces. FILOMAT 26(2), 407–414 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  21. Matthews, S.G.: Partial metric topology. In: Proc. 8th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci., vol. 728, pp. 183–197 (1994)

  22. Nashine, H.K., Kadelburg, Z.: Common fixed point theorems under weakly Hardy–Rogers-type contraction conditions in ordered orbitally complete metric spaces. RASCAM (1007) (2012). doi:10.1007/s13398-012-0106-2

  23. Nashine, H.K., Kadelburg, Z., Golubovic, Z.: Common fixed point results using generalized distances on orbitally complete ordered metric spaces. J. Appl. Math. (2012)

  24. Romaguera, S.: A Kirk type characterization of completeness for partial metric spaces. Fixed Point Theory Appl. (2010). doi:10.1155/2010/493298

    MATH  MathSciNet  Google Scholar 

  25. Shukla, S., Radenović, S.: Some common fixed point theorems for \(F\)-contraction type mappings in \(0\)-complete partial metric spaces. J. Math. (2013)

  26. Shukla, S., Radenović, S., Kadelburg, Z.: Some fixed point theorems for ordered \(f\)-orbitally complete partial metric spaces. Theory Appl. Math. Comput. Sci. 4(1), 87–98 (2014)

    MATH  Google Scholar 

  27. Sastry, K.P.R., Naidu, S.V.R., Rao, I.H.N., Rao, K.P.R.: Common fixed points for asymptotically regular mappings. Indian J. Pure Appl. Math. 15, 849–854 (1984)

    MathSciNet  Google Scholar 

  28. Shukla, S., Radenović, S., Vetro, C.: Set-valued Hardy-Rogers type contraction in \(0\)-complete partial metric spaces. Int. J. Math. Math. Sci. (2014)

  29. Valero, O.: On Banach fixed point theorems for partial metric spaces. Appl. Gen. Topol. 6, 229–240 (2005)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The fourth author is thankful to the Ministry of Science and Technological Development of Serbia. Poom Kumam was supported by the Higher Education Research Promotion and National Research University Project of Thailand (NRU57000621).

Author information

Authors and Affiliations

  1. Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Mandir Hasaud, Raipur, 492101, Chhattisgarh, India

    Hemant Kumar Nashine

  2. Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani, 12121, Thailand

    Wutiphol Sintunavarat

  3. Faculty of Mathematics, University of Belgrade, Studentski trg 16, Beograd, 11000, Serbia

    Zoran Kadelburg

  4. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam

Authors
  1. Hemant Kumar Nashine
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wutiphol Sintunavarat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zoran Kadelburg
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Poom Kumam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Poom Kumam.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nashine, H.K., Sintunavarat, W., Kadelburg, Z. et al. Fixed point theorems in orbitally \(0\)-complete partial metric spaces via rational contractive conditions. Afr. Mat. 26, 1121–1136 (2015). https://doi.org/10.1007/s13370-014-0269-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-014-0269-4

Keywords

Mathematics Subject Classification (2000)

Search

Navigation