International Journal of Nonlinear Analysis and Applications

Some fixed point theorems satisfying generalized contraction conditions in dislocated quasi metric space

Document Type : Research Paper

Authors

1 Department of Sciences (Mathematics), Manav Rachna University, Faridabad-121004, India

2 Department of Mathematics, Ram Lal Anand College, University of Delhi, South Campus, Anand Niketan, Delhi-110021, India

3 Department of Applied Sciences and Humanities, IMS Engineering College, Ghaziabad, Uttar Pradesh-201015, India

Abstract

The goal of this research article is to study some fixed point results in dislocated quasi metric spaces. These results are proved for certain generalized contraction conditions involving linear and rational expressions. Our results extend and generalize some of the well-known fixed point results of the literature available in fixed point theory. Suitable examples of the established results are also given.

Keywords

[1] C.T. Aage and J.N. Salunke, Some results of fixed point theorem in dislocated quasi-metric spaces, Bull. Marathadawa Math. Soc. 9 (2008), 1–5.
[2] L.B. Ciric, A generalization of Banach’s contraction principle, Proc. Am. Math. Soc. 45 1974, 267–273.
[3] B.K. Dass and S. Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math. 6 (1975), no. 12, 1455–1458.
[4] P. Hitzler and A.K. Seda, Dislocated topologies, J. Electr. Eng. 51 (2000), no. 12, 3–7.
[5] P. Hitzler, Generalized metrics and topology in logic programming semantics, PhD Thesis, National University of Ireland, 2001.
[6] A. Isufati, Fixed point theorems in dislocated quasi-metric space, Appl. Math. Sci. 4 (2010), no. 5, 217–233.
[7] R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc. 60 (1968), 71–76.
[8] M. Kohli, R. Shrivastava, and M. Sharma, Some results on fixed point theorems in dislocated quasi metric space, Int. J. Theor. Appl. Sci. 2 (2010), 27–28.
[9] S.G. Mathews, Metrics domain for completeness, PhD Thesis, Department of Computer Science, University of Warwick, UK, 1986.
[10] S.T. Patel and M. Patel, Some results of fixed point theorem in dislocated quasi-metric space, Int. J. Res. Mod. Eng. Technol. 1 (2013), 20–24.
[11] M.U. Rahman and M. Sarwar, Fixed point results in dislocated quasi-metric spaces, Int. Math. Forum 9 (2014), 677–682.
[12] A.K. Seda, Quasi metrics and the semantics of logic programs, Fund. Inf. 29 (1997), 97–117.
[13] F.M. Zeyada, G.H. Hassan, and M.A. Ahmed, A generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi metric spaces, Arab. J. Sci. Engg. 31 (2006), no. 1A, 111–114.
[14] K. Zoto, E. Houxha, and A. Isufati, Some new results in dislocated and dislocated quasi metric spaces, Appl. Math. Sci. 6 (2012), 3519–3526.
International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 1
January 2025
Pages 245-251
  • Receive Date: 20 August 2022
  • Accept Date: 13 October 2023