International Journal of Nonlinear Analysis and Applications

Coupled fixed point theorems in partially ordered complex valued metric spaces with application

Document Type : Research Paper

Authors

1 Department of mathematics, Farhangian university, Iran.

2 Department of Mathematics, Semnan University, Iran

3 Departement of Mathematics, Amirkabir University of Technology, Iran

Abstract

In this paper, we prove some coupled fixed point theorems for nonlinear contraction type mappings in complete complex valued metric spaces endowed with partial order. We support our results by establishing an illustrative example. Also we give an application of this results to the solution of the Urysohn type integral equations. 

Keywords

[1] M. Abbas, M. Arshad and A. Azam, Fixed points of asymptotically regular mappings in complex valued metric spaces, Georgian Math. J. 20 (2013), no. 2, 213–221.
[2] A. Azam, J. Ahmad and P. Kumam, Common fixed point theorems for multi valued mappings in complex valued metric spaces, J. Inequal. Appl. 578 (2013).
[3] A. Azam, F. Brian and M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Func. Anal. Optim. 32 (2011), no. 3, 243–253.
[4] T.G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379–1393.
[5] M. Borcut and V. Berinde, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Appl. Math. Comput. 218 (2012), 5929–5936.
[6] M. Eshaghi Gordji, H. Baghani and Y.J. Cho, Coupled fixed point theorems for contractions in intuitionistic fuzzy normed spaces, Math. Comput. Modell. 54 (2011), no. 9, 1897–1906.
[7] M. Eshaghi Gordji, M. Paknazar, M. De La Sen and S. M. Vaezpour, N-fixed point theorem for nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl. 111 (2013).
[8] V. Lakshmikantham and L. Ciri´c, ´ Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), 4341–4349.
[9] S.K. Mohanta and R. Maitra, Common fixed points of three self mapping in complex valued metric spaces, Int. J. Math. Arch. 3 (2012), no. 8, 2946–2953.
[10] F. Rouzkard and M. Imdad, Some common fixed point theorems on complex valued metric spaces, Comput. Math. Appl. 64 (2012), no. 6, 1866–1874.
[11] B. Samet and C. Vetro, Coupled fixed point, f-invariant set and fixed point of N−order, Ann. Funct. Anal. 1 (2010), no. 2, 46–56.
[12] W. Sintunavarat and P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequal. Appl. 84 (2012).
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 13-20
  • Receive Date: 04 July 2014
  • Accept Date: 27 December 2017