Korean J. Math. Vol. 26 No. 4 (2018) pp.809-822
DOI: https://doi.org/10.11568/kjm.2018.26.4.809

Complex valued dislocated metric spaces

Main Article Content

Ozgur Ege
Ismet Karaca

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.


Article Details

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. Google Scholar

[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. Google Scholar

[3] S. Banach, Sur les operations dans les ensembles abstraits et leurs applications aux equations integrales, Fund. Math. 3 (1922), 133–181. Google Scholar

[4] A. Batool, T. Kamran, S.Y. Jang, C. Park, Generalized φ-weak contractive fuzzy mappings and related fixed point results on complete metric space, J. Comput. Anal. Appl. 21 (4) (2016), 729–737. Google Scholar

[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. Google Scholar

[6] O. Ege, Complex valued rectangular b-metric spaces and an application to linear equations, J. Nonlinear Sci. Appl. 8 (6) (2015), 1014–1021. Google Scholar

[7] O. Ege, Complex valued Gb-metric spaces, J. Comput. Anal. Appl. 21 (2) (2016), 363–368. Google Scholar

[8] O. Ege, Some fixed point theorems in complex valued Gb-metric spaces, J. Non-linear Convex Anal. 18 (11) (2017), 1997–2005. Google Scholar

[9] O. Ege and I. Karaca, Banach fixed point theorem for digital images, J. Nonlinear Sci. Appl. 8 (3) (2015), 237–245. Google Scholar

[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. Google Scholar

[11] P. Hitzler, Generalized metrics and topology in logic programming semantics, Ph.D Thesis, National University of Ireland, University College Cork, 2001. Google Scholar

[12] P. Hitzler and A.K. Seda, Dislocated topologies, J. Electr. Eng. 51 (2000), 3–7. Google Scholar

[13] Sh. Jain, Sh. Jain and L.B. Jain, On Banach contraction principle in a conemetric space, J. Nonlinear Sci. Appl. 5 (2012), 252–258. Google Scholar

[14] K. Jha and D. Panthi, A common fixed point theorem in dislocated metric space, Appl. Math. Sci. 6 (2012), 4497–4503. Google Scholar

[15] M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014:38 (2014). Google Scholar

[16] M. Nazam, M. Arshad and C. Park, Fixed point theorems for improved α-Geraghty contractions in partial metric spaces, J. Nonlinear Sci. Appl. 9(6) (2016), 4436–4449. Google Scholar

[17] L. Pasicki, Dislocated metric and fixed point theorems, Fixed Point Theory Appl. 2015:82 (2015). Google Scholar

[18] M.U. Rahman and M. Sarwar, Fixed point theorems for expanding mappings in dislocated metric space, Math. Sci. Lett. 4 (2015), 69–73. Google Scholar

[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. Google Scholar

[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. Google Scholar

[21] F. Rouzkard and M. Imdad, Some common fixed point theorems on complex valued metric spaces, Comput. Math. Appl. 64 (6) (2012), 1866–1874. Google Scholar

[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. Google Scholar

[23] W. Sintunavarat and P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequal. Appl. 2012:84 (2012). Google Scholar

[24] K. Sitthikul and S. Saejung, Some fixed point theorems in complex valued metric spaces, Fixed Point Theory Appl. 2012:189 (2012). Google Scholar

[25] J. Sun and X. Han, The Banach fixed point theorem application to Hopf bifurcation of a generalized Boussinesq system, Adv. Difference Equ. 2015:43 (2015). Google Scholar

[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. Google Scholar