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Vietnam Journal of Mathematics

, Volume 43, Issue 4, pp 793–800 | Cite as

Two Suzuki Type Fixed Point Theorems on Partial Metric Spaces

  • Özlem AcarEmail author
  • Ishak Altun
Article
  • 182 Downloads

Abstract

Recently, Paesano and Vetro (Topol. Appl. 159: 911–920, 2012) have been studied Suzuki type fixed point theorem on partial metric spaces. In this paper, we will give Kannan type of this theorem on partial metric spaces.

Keywords

Fixed point Contraction mapping Complete partial metric space 

Mathematics Subject Classification (2010)

Primary 54H25 Secondary 47H10 

Notes

Acknowledgments

The authors are thankful to referees for making valuable suggestions leading to the better presentation of the paper.

References

  1. 1.
    Altun, I., Sola, F., Simsek, H.: Generalized contractions on partial metric spaces. Topol. Appl. 157, 2778–2785 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Abbas, M., Basit, A.: Fixed point of Suzuki–Zamfirescu hybrid contractions in partial metric spaces via partial Hausdorff metric. Fixed Point Theory Appl. 2013, 21 (2013)CrossRefGoogle Scholar
  3. 3.
    Connell, E.H.: Properties of fixed point spaces. Proc. Am. Math. Soc. 10, 974–979 (1959)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Ðorić, D., Kadelburg, Z., Radenović, S.: Edelstein–Suzuki-type fixed point results in metric and abstract metric spaces. Nonlinear Anal. 75, 1927–1932 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Escardó, M.H.: Pcf extended with real numbers. Theor. Comput. Sci. 162, 79–115 (1996)zbMATHCrossRefGoogle Scholar
  6. 6.
    Haghi, R.H., Rezapour, Sh., Shahzad, N.: Be careful on partial metric fixed point results. Topol. Appl. 160, 450–454 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Imdad, M., Erduran, A.: Suzuki type generalization of Chatterjea contraction mappings of complete partial metric space. J. Oper. 2013, 923843 (2013)Google Scholar
  8. 8.
    Kannan, R.: Some results on fixed points-II. Am. Math. Mont. 76, 405–408 (1969)zbMATHCrossRefGoogle Scholar
  9. 9.
    Kirk, W.A.: Caristi’s fixed point theorem and metric convexity. Colloq. Math. 36, 81–86 (1976)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Kikkawa, M., Suzuki, T.: Some similarity between contractions and Kannan mappings. Fixed Point Theory Appl. 2008, 649749 (2008)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Kikkawa, M., Suzuki, T.: Some notes on fixed point theorems with constants. Bull. Kyushu Inst. Tech. Pure Appl. Math. 56, 11–18 (2009)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Kikkawa, M., Suzuki, T.: Three fixed point theorems for generalized contractions with constants in complete metric spaces. Nonlinear Anal. 69, 2942–2949 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Ćirić, Lj.B., Abbas, M., Rajović, M., Ali, B.: Suzuki type fixed point theorems for generalized multi-valued mappings on a set endowed with two b-metrics. Appl. Math. Comput. 219, 1712–1723 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Matthews, S.G.: Partial metric topology. Ann. New York Acad. Sci. 728, 183–197 (1994)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Popescu, O.: Fixed point theorems in metric spaces. Bull. Transilv. Univ. Braşov 50, 479–482 (2008)Google Scholar
  16. 16.
    Popescu, O.: Two fixed point theorems for generalized contractions with constants in complete metric space. Cent. Eur. J. Math. 7, 529–538 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Paesano, D., Vetro, P.: Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces. Topol. Appl. 159, 911–920 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Romaguera, S.: On Nadler’s fixed point theorem for partial metric spaces. Math. Sci. Appl. E-Notes 1, 1–8 (2013)MathSciNetGoogle Scholar
  19. 19.
    Samet, B., Vetro, C., Vetro, F.: From metric spaces to partial metric spaces. Fixed Point Theory Appl. 2013, 5 (2013)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Subrahmanyam, P.V.: Completeness and fixed-points. Monats. Math. 80, 325–330 (1975)zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Suzuki, T.: A generalized Banach contraction principle that characterizes metric completeness. Proc. Am. Math. Soc. 136, 1861–1869 (2008)zbMATHCrossRefGoogle Scholar
  22. 22.
    Valero, O.: On Banach fixed point theorems for partial metric spaces. Appl. Gen. Topol. 6, 229–240 (2005)zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and ArtsKirikkale UniversityYahsihanTurkey

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