Some fixed point results on complex valued \(G_{b}\)-metric spaces

  • Arslan Hojat Ansari
  • Ozgur Ege
  • Stojan Radenović
Original Paper


In this paper, we prove some fixed point theorems for new type generalized contractive mappings involving \({ C }\) -class function in complex valued \(G_b\)-metric spaces. The obtained results generalize and improve some fixed point results in the literature.


Fixed point C-class function Complex valued \(G_{b}\)-metric space 

Mathematics Subject Classification

Primary 47H10 Secondary 54H25 



The authors express their sincere gratitude to the anonymous referees for their careful reading and suggestions that improved the presentation of this paper.


  1. 1.
    Abbas, M., Nazir, T., Vetro, P.: Common fixed point results for three maps in \(G\)-metric spaces. Filomat 25(4), 1–17 (2011)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Agarwal, R.P., Kadelburg, Z., Radenović, S.: On coupled fixed point results in asymmetric \(G\)-metric spaces. J. Inequal. Appl. 2013, 528 (2013)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Ansari, A.H.: Note on \(\varphi -\psi \)-contractive type mappings and related fixed point. In: The 2nd Regional Conference on Mathematics And Applications, Payame Noor University, pp. 377–380 (2014)Google Scholar
  4. 4.
    Ansari, A.H., Chandok, S., Ionescu, C.: Fixed point theorems on \(b\)-metric spaces for weak contractions with auxiliary functions. J. Inequal. Appl. 2014, 429 (2014)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Ansari, A.H., Muzeyyen, Sangurlu, Turkoglu, D.: Coupled fixed point theorems for mixed G-monotone mappings in partially ordered metric spaces via new functions. Gazi Univ. J. Sci. 29(1), 149–158 (2016)Google Scholar
  6. 6.
    Aydi, H., Shatanawi, W., Vetro, C.: On generalized weakly \(G\)-contraction mapping in \(G\)-metric spaces. Comput. Math. Appl. 62, 4222–4229 (2011)CrossRefMATHGoogle Scholar
  7. 7.
    Azam, A., Fisher, B., Khan, M.: Common fixed point theorems in complex valued metric spaces. Numer. Funct. Anal. Optim. 32, 243–253 (2011)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Aghajani, A., Abbas, M., Roshan, J.R.: Common fixed point of generalized weak contractive mappings in partially ordered \(G_b\)-metric spaces. Filomat 28(6), 1087–1101 (2014)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Bakhtin, I.A.: The contraction mapping principle in quasimetric spaces. Funct. Anal. Unianowsk Gos. Ped. Inst. 30, 26–37 (1989)Google Scholar
  10. 10.
    Boriceanu, M., Bota, M., Petrusel, A.: Multivalued fractals in \(b\)-metric spaces. Cent. Eur. J. Math. 8(2), 367–377 (2010)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Chandok, S., Tas, K., Ansari, A.H.: Some fixed point results for TAC-type contractive mappings. J. Funct. Spaces. 2016, 1907676 (2016). doi: 10.1155/2016/1907676
  12. 12.
    Czerwik, S.: Contraction mappings in \(b\)-metric spaces. Acta. Math. Inform. Univ. Ostraviensis 1, 5–11 (1993)MathSciNetMATHGoogle Scholar
  13. 13.
    Ege, O.: Complex valued \(G_{b}\)-metric spaces. J. Comput. Anal. Appl. 21(2), 363–368 (2016)MathSciNetMATHGoogle Scholar
  14. 14.
    Ege, O.: Some fixed point theorems in complex valued \(G_{b}\)-metric spaces. J. Nonlinear Convex Anal. (2016, accepted)Google Scholar
  15. 15.
    Fadail, Z.M., Ahmad, A.G.B., Ansari, A.H., Radenović, S., Rajović, M.: Some common fixed point results of mappings in 0-complete metric-like spaces via new function. Appl. Math. Sci. 9, 4109–4127 (2015)Google Scholar
  16. 16.
    Isik, H., Ansari, A.H., Turkoglu, D., Chandok, S.: Common fixed points for \((\psi, F,\alpha,\beta )\)-weakly contractive mappings in generalized metric spaces via new functions. Gazi Univ. J. Sci. 28(4), 703–708 (2015)Google Scholar
  17. 17.
    Kang, S.M., Singh, B., Gupta, V., Kumar, S.: Contraction principle in complex valued \(G\)-metric spaces. Int. J. Math. Anal. 7(52), 2549–2556 (2013)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Latif, A., Isik, H., Ansari, A.H.: Fixed points and functional equation problems via cyclic admissible generalized contractive type mappings. J. Nonlinear Sci. Appl. 9, 1129–1142 (2016)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Liu, X.-I., Ansari, A.H., Chandok, S., Park, C.: Some new fixed point results in partial ordered metric spaces via admissible mappings and two new functions. J. Nonlinear Sci. Appl. 9, 1564–1580 (2016)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Mustafa, Z., Sims, B.: A new approach to a generalized metric spaces. J. Nonlinear Convex Anal. 7, 289–297 (2006)MathSciNetMATHGoogle Scholar
  21. 21.
    Mustafa, Z., Sims, B.: Fixed point theorems for contractive mappings in complete \(G\)-metric spaces. Fixed Point Theory Appl. 2009, 917175 (2009)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Mustafa, Z., Roshan, J.R., Parvaneh, V.: Coupled coincidence point results for \((\psi,\varphi )\)-weakly contractive mappings in partially ordered \(G_b\)-metric spaces. Fixed Point Theory Appl. 2013, 206 (2013)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Mustafa, Z., Roshan, J.R., Parvaneh, V.: Existence of tripled coincidence point in ordered \(G_b\)-metric spaces and applications to a system of integral equations. J. Inequal. Appl. 2013, 453 (2013)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Parvaneh, V., Roshan, J.R., Radenović, S.: Existence of tripled coincidence points in ordered \(b\)-metric spaces and an application to a system of integral equations. Fixed Point Theory Appl. 2013, 130 (2013)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Rao, K.P.R., BhanuLakshmi, K., Mustafa, Z., Raju, V.C.C.: Fixed and related fixed point theorems for three maps in \(G\)-metric spaces. J. Adv. Stud. Topol. 3(4), 12–19 (2012)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Rao, K.P.R., Swamy, P.R., Prasad, J.R.: A common fixed point theorem in complex valued \(b\)-metric spaces. Bull. Math. Stat. Res. 1(1), 1–8 (2013)MathSciNetGoogle Scholar
  27. 27.
    Saadati, R., Vaezpour, S.M., Vetro, P., Rhoades, B.E.: Fixed point theorems in generalized partially ordered \(G\)-metric spaces. Math. Comput. Model. 52, 797–801 (2010)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Sedghi, S., Shobkolaei, N., Roshan, J.R., Shatanawi, W.: Coupled fixed point theorems in \(G_b\)-metric spaces. Mat. Vesnik 66(2), 190–201 (2014)MathSciNetMATHGoogle Scholar
  29. 29.
    Shatanawi, W.: Fixed point theory for contractive mappings satisfying \(\Phi \)-maps in \(G\)-metric spaces. Fixed Point Theory Appl. 2010, 181650 (2010)MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Wang, S., Ansari, A.H., Chandok, S.: Some fixed point results for non-decreasing and mixed monotone mappings with auxiliary functions. Fixed Point Theory Appl. 2015, 209 (2015)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Italia 2017

Authors and Affiliations

  • Arslan Hojat Ansari
    • 1
  • Ozgur Ege
    • 2
  • Stojan Radenović
    • 3
  1. 1.Department of MathematicsKaraj Branch, Islamic Azad UniversityKarajIran
  2. 2.Department of MathematicsManisa Celal Bayar UniversityManisaTurkey
  3. 3.Faculty of Mechanical EngineeringUniversity of BelgradeBelgradeSerbia

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