Advertisement

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

  • Zoran D. Mitrović
  • Hassen Aydi
  • Zoran Kadelburg
  • Ghasem Soleimani RadEmail author
Article
  • 5 Downloads

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.

Keywords

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

Mathematics Subject Classification

Primary 47H10 Secondary 55M20 

Notes

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)Google Scholar
  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 CrossRefGoogle Scholar
  4. 4.
    Aydi, H., Czerwik, S.: Fixed point theorems in generalized \(b\)-metric spaces. Modern Discrete Math. Anal. 131, 1–9 (2018)MathSciNetCrossRefGoogle 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)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Czerwik, S.: Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostrav. 1, 5–11 (1993)MathSciNetzbMATHGoogle 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)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Fisher, B.: A note on a theorem of Khan. Rend. Ist. Mat. Univ. Trieste 10, 1–4 (1978)MathSciNetzbMATHGoogle 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)MathSciNetCrossRefGoogle 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)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Jaggi, D.S.: Some unique fixed point theorems. Indian J. Pure. Appl. Math. 8, 223–230 (1977)MathSciNetzbMATHGoogle 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)Google Scholar
  14. 14.
    Karapinar, E.: Some fixed points results on Branciari metric spaces via implicit functions. Carpathian J. Math. 31(3), 339–348 (2015)MathSciNetzbMATHGoogle 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)MathSciNetzbMATHGoogle 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)Google Scholar
  17. 17.
    Khan, M.S.: A fixed point theorem for metric spaces. Rend. Inst. Math. Univ. Trieste 8, 69–72 (1976)zbMATHGoogle 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)MathSciNetCrossRefGoogle 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)MathSciNetCrossRefGoogle 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)CrossRefGoogle 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)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2019

Authors and Affiliations

  • Zoran D. Mitrović
    • 1
    • 2
  • Hassen Aydi
    • 3
    • 4
  • Zoran Kadelburg
    • 5
  • Ghasem Soleimani Rad
    • 6
    Email author
  1. 1.Nonlinear Analysis Research GroupTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Institut Supérieur d’Informatique et des Techniques de CommunicationUniversité de SousseH. SousseTunisia
  4. 4.China Medical University HospitalChina Medical UniversityTaichungTaiwan
  5. 5.Faculty of MathematicsUniversity of BelgradeBeogradSerbia
  6. 6.Young Researchers and Elite club, West Tehran BranchIslamic Azad UniversityTehranIran

Personalised recommendations