Coupled Fixed Point Theorem in Dislocated Quasi b­-Metric Spaces

Document Type: Original Article

Authors

1 Department of Mathematics, Government PG Jahanzeb College Saidu Sharief Swat, Khyber PakhtunKhwa, Pakistan.

2 Department of Mathematics, University of Malakand, Dir(L), Khyber PakhtunKhwa, Pakistan.

Abstract

In this paper, we de ne the notion of a coupled coincidence fixed point and prove a coupled coincidence fixed
point theorem in dislocated quasi b-metric space. In order to validate our main result and its corollaries an
example is given

Keywords


[1] D. Akcay, C. Alaca, Coupled fixed point theorem in dislocated quasi-metric space, J. Adv. Stud. Topol., 4 (2012),
66-72.

[2] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorem in partially ordered metric spaces and applications,
Nonlinear Anal., 65 (2006), 1379-1393.

[3] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11.

[4] M. Kir, H. Kizitune, On some well-known fixed point theorems in b-metric space, Turkish J. Anal. Number Theory,
1 (2013), 13-16.

[5] M.U. Rahman, M. Sarwar, Dislocated quasi b-metric space and fixed point theorems, Electron. J. Math. Anal.
Appl., 4 (2016), 16-24.

[6] M.U. Rahman, M. Sarwar, Coupled fixed point theorem for rational type contraction conditions in dislocated
quasi-metric space, Palestine J. Math., 5 (2016), 6-11.

[7] M.U. Rahman, M. Sarwar, P.S. Kumari, Common tripled fixed point theorem in dislocated quasi-metric space,
Sindh Univ. Res. J., (Science Series), 47 (2015), 649-652.

[8] M. Sarwar, M.U. Rahman, Fixed point theorems for Ciric's and generalized contractions in b-metric spaces, Int.
J. Anal. Appl., 7 (2015), 70-78. 

[9] M. Sarwar, M.U. Rahman, G. Ali, Some xed point results in dislocated quasi-metric (dq-metric) spaces, J.
Inequal. Appl., 2014 (2014), 11 pages. 

[10] S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math., 11 (2014), 703-711.

[11] F.M. Zeyada, G.F. Hassan, M.A. Ahmed, A Generalization of fixed point theorem due to Hitzler and Seda in
dislocated quasi-metric space, Arabian J. Sci. Engg., 31 (2005), 111-114.