On some rational contractions in \(\mathbf {b_{v}(s)}\)-metric spaces

Abstract

In this paper, we prove versions of Khan type and Dass–Gupta type contraction principles in \(b_{v}(s)\)-metric spaces. The results which we obtain generalize many known results in fixed point theory. Examples show how these results can be applied in concrete situations.

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

References

  1. 1.

    Ahmad, J., Arshad, M., Vetro, C.: On a theorem of Khan in a generalized metric space. Int. J. Anal. Article ID 852727, p 6 (2013)

  2. 2.

    Ansari, A.H., Aydi, H., Kumari, P.S., Yildirim, I.: New fixed point results via \(C\)-class functions in \(b\)-rectangular metric spaces. Commun. Math. Anal. 9(2), 109–126 (2018)

    Google Scholar 

  3. 3.

    Aydi, H., Chen, C.M., Karapinar, E.: Interpolative Ciric-Reich-Rus type contractions via the Branciari distance. Mathematics 7(1), 84 (2019). https://doi.org/10.3390/math7010084

    Article  Google Scholar 

  4. 4.

    Aydi, H., Czerwik, S.: Fixed point theorems in generalized \(b\)-metric spaces. Modern Discrete Math. Anal. 131, 1–9 (2018)

    MathSciNet  Article  Google Scholar 

  5. 5.

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

    Google Scholar 

  6. 6.

    Branciari, A.: A fixed point theorem of Banach–Caccioppoli type on a class of generalized metric spaces. Publ. Math. Debr. 57, 31–37 (2000)

    MathSciNet  MATH  Google Scholar 

  7. 7.

    Czerwik, S.: Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostrav. 1, 5–11 (1993)

    MathSciNet  MATH  Google Scholar 

  8. 8.

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

    MathSciNet  MATH  Google Scholar 

  9. 9.

    Fisher, B.: A note on a theorem of Khan. Rend. Ist. Mat. Univ. Trieste 10, 1–4 (1978)

    MathSciNet  MATH  Google Scholar 

  10. 10.

    George, R., Radenović, S., Reshma, K.P., Shukla, S.: Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 8, 1005–1013 (2015)

    MathSciNet  Article  Google Scholar 

  11. 11.

    Gulyaz, S., Karapinar, E., Erhan, I.M.: Generalized \(\alpha \)-Meir–Keeler contraction mappings on Branciari b-metric spaces. Filomat 31(17), 5445–5456 (2017)

    MathSciNet  Article  Google Scholar 

  12. 12.

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

    MathSciNet  MATH  Google Scholar 

  13. 13.

    Jovanović, M., Kadelburg, Z., Radenović, S.: Common fixed point results in metric-type spaces. Fixed Point Theory Appl. Article ID 978121, p 15 (2010)

  14. 14.

    Karapinar, E.: Some fixed points results on Branciari metric spaces via implicit functions. Carpathian J. Math. 31(3), 339–348 (2015)

    MathSciNet  MATH  Google Scholar 

  15. 15.

    Karapinar, E., Pitea, A.: On \(\alpha \)-\(\psi \)-Geraghty contraction type mappings on quasi-Branciari metric spaces. J. Nonlinear Convex Anal. 17(7), 1291–1301 (2016)

    MathSciNet  MATH  Google Scholar 

  16. 16.

    Karapınar, E., Czerwik, S., Aydi, H.: \((\alpha ,\psi )\)-Meir–Keeler contraction mappings in generalized b-metric spaces. J. Funct. Spaces. Article ID 3264620, p 4 (2018)

  17. 17.

    Khan, M.S.: A fixed point theorem for metric spaces. Rend. Inst. Math. Univ. Trieste 8, 69–72 (1976)

    MATH  Google Scholar 

  18. 18.

    Mitrović, Z.D., Radenović, S.: The Banach and Reich contractions in \(b_{v}(s)\)-metric spaces. J. Fixed Point Theory Appl. 19, 3087–3095 (2017)

    MathSciNet  Article  Google Scholar 

  19. 19.

    Mustafa, Z., Karapinar, E., Aydi, H.: A discussion on generalized almost contractions via rational expressions in partially ordered metric spaces. J. Inequal. Appl. 2014, 219 (2014)

    MathSciNet  Article  Google Scholar 

  20. 20.

    Piri, H., Rahrovi, S., Kumam, P.: Khan type fixed point theorems in a generalized metric space. J. Math. Comput. Sci. 16, 211–217 (2016)

    Article  Google Scholar 

  21. 21.

    Roshan, J.R., Parvaneh, V., Kadelburg, Z., Hussain, N.: New fixed point results in \(b\)-rectangular metric spaces. Nonlinear Anal. Model. Control 21(5), 614–634 (2016)

    MathSciNet  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ghasem Soleimani Rad.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mitrović, Z.D., Aydi, H., Kadelburg, Z. et al. On some rational contractions in \(\mathbf {b_{v}(s)}\)-metric spaces. Rend. Circ. Mat. Palermo, II. Ser 69, 1193–1203 (2020). https://doi.org/10.1007/s12215-019-00465-6

Download citation

Keywords

  • Fixed point
  • b-metric space
  • Rectangular metric space
  • \(b_{v}(s)\)-metric space

Mathematics Subject Classification

  • Primary 47H10
  • Secondary 55M20