DOI QR코드

DOI QR Code

COMPLEX VALUED DISLOCATED METRIC SPACES

  • Ege, Ozgur (Department of Mathematics, Ege University) ;
  • Karaca, Ismet (Department of Mathematics, Ege University)
  • Received : 2018.08.25
  • Accepted : 2018.12.17
  • Published : 2018.12.30

Abstract

In this paper, we introduce complex valued dislocated metric spaces. We prove Banach contraction principle, Kannan and Chatterjea type fixed point theorems in this new space. Moreover, we give some applications of the results to differential equations and iterated functions.

Keywords

References

  1. C.T. Aage and J.N. Salunke, The results on fixed point theorems in dislocated and dislocated quasi-metric space, Appl. Math. Sci. 2 (2008), 2941-2948.
  2. A. Azam, B. Fisher and M. Khan, Common fixed point theorems in complex valued metric spaces, Number. Funct. Anal. Optim. 32 (2011), 243-253. https://doi.org/10.1080/01630563.2011.533046
  3. S. Banach, Sur les operations dans les ensembles abstraits et leurs applications aux equations integrales, Fund. Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
  4. A. Batool, T. Kamran, S.Y. Jang, C. Park, Generalized $\phi$-weak contractive fuzzy mappings and related fixed point results on complete metric space, J. Comput. Anal. Appl. 21 (4) (2016), 729-737.
  5. S. Bhatt, S. Chaukiyal and R.C. Dimri, Common fixed point of mappings satisfying rational inequality in complex valued metric space, Int. J. Pure Appl. Math. 73(2) (2011), 159-164.
  6. O. Ege, Complex valued rectangular b-metric spaces and an application to linear equations, J. Nonlinear Sci. Appl. 8 (6) (2015), 1014-1021. https://doi.org/10.22436/jnsa.008.06.12
  7. O. Ege, Complex valued Gb-metric spaces, J. Comput. Anal. Appl. 21 (2) (2016), 363-368.
  8. O. Ege, Some fixed point theorems in complex valued Gb-metric spaces, J. Nonlinear Convex Anal. 18 (11) (2017), 1997-2005.
  9. O. Ege and I. Karaca, Banach fixed point theorem for digital images, J. Nonlinear Sci. Appl. 8 (3) (2015), 237-245.
  10. M. Eshaghi Gordji, S. Pirbavafa, M. Ramezani and C. Park, Presic-Kannan-Rus fixed point theorem on partially ordered metric spaces, Fixed Point Theory 15 (2) (2014), 463-474.
  11. P. Hitzler, Generalized metrics and topology in logic programming semantics, Ph.D Thesis, National University of Ireland, University College Cork, 2001.
  12. P. Hitzler and A.K. Seda, Dislocated topologies, J. Electr. Eng. 51 (2000), 3-7.
  13. Sh. Jain, Sh. Jain and L.B. Jain, On Banach contraction principle in a cone metric space, J. Nonlinear Sci. Appl. 5 (2012), 252-258. https://doi.org/10.22436/jnsa.005.04.01
  14. K. Jha and D. Panthi, A common fixed point theorem in dislocated metric space, Appl. Math. Sci. 6 (2012), 4497-4503.
  15. M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014).
  16. M. Nazam, M. Arshad and C. Park, Fixed point theorems for improved ${\alpha}$-Geraghty contractions in partial metric spaces, J. Nonlinear Sci. Appl. 9(6) (2016), 4436-4449. https://doi.org/10.22436/jnsa.009.06.83
  17. L. Pasicki, Dislocated metric and fixed point theorems, Fixed Point Theory Appl. 2015:82 (2015).
  18. M.U. Rahman and M. Sarwar, Fixed point theorems for expanding mappings in dislocated metric space, Math. Sci. Lett. 4 (2015), 69-73.
  19. K.P.R. Rao and P. Rangaswamy, A coincidence point theorem for four mappings in dislocated metric spaces, Int. J. Contemp. Math. Sci. 6 (2011), 1675-1680.
  20. K.P.R. Rao, P.R. Swamy and J.R. Prasad, A common fixed point theorem in complex valued b-metric spaces, Bull. Math. Stat. Res. 1 (1) (2013), 1-8.
  21. F. Rouzkard and M. Imdad, Some common fixed point theorems on complex valued metric spaces, Comput. Math. Appl. 64 (6) (2012), 1866-1874. https://doi.org/10.1016/j.camwa.2012.02.063
  22. W. Shatanawi and H.K. Nashine, A generalization of Banach's contraction principle for nonlinear contraction in a partial metric space, J. Nonlinear Sci. Appl. 5 (2012), 37-43. https://doi.org/10.22436/jnsa.005.01.05
  23. W. Sintunavarat and P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequal. Appl. 2012:84 (2012).
  24. K. Sitthikul and S. Saejung, Some fixed point theorems in complex valued metric spaces, Fixed Point Theory Appl. 2012:189 (2012).
  25. J. Sun and X. Han, The Banach fixed point theorem application to Hopf bifurcation of a generalized Boussinesq system, Adv. Di erence Equ. 2015:43 (2015).
  26. F.M. Zeyada, G.H. Hassan and M.A. Ahmad, A generalization of fixed point theorem due to Hitzler and Seda in dislocated quasi-metric space, Arabian J. Sci. Eng. 31 (2005), 111-114.

Cited by

  1. FIXED POINT THEOREMS IN COMPLEX VALUED CONVEX METRIC SPACES vol.26, pp.1, 2018, https://doi.org/10.22771/nfaa.2021.26.01.09
  2. Common fixed point results for multi-valued mappings in complex-valued double controlled metric spaces and their applications to the existence of solution of fractional integral inclusion systems vol.154, pp.None, 2018, https://doi.org/10.1016/j.chaos.2021.111622