Document Type: Research Paper

Authors

1 Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar, Guntur-522 510, Andhra Pradesh, India

2 Department of Mathematics, K L University, Vaddeswaram, Guntur-522 502, Andhra Pradesh, India

3 Department of Mathematics, Sir C R R College of Engineering, Eluru, West Godavari-534 007, Andhra Pradesh, India

Abstract

In this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $S_b$-metric spaces satisfying a contrctive type condition. We furnish an example to support our main theorem. We also give a corollary for Junck type maps.

Keywords

Main Subjects

###### ##### References

[1] M. Abbas, M. Ali khan, S. Randenovic, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput. 217 (2010), 195-202.

[2] S. Czerwik, Contraction mapping in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis, 1 (1993), 5-11.

[3] T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis. Theory, Methods and Applications, 65 (7) (2006), 1379-1393.

[4] V. Lakshmikantham, L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis. Theory, Methods and Applications, 70 (12) (2009), 4341-4349.

[5] H. Rahimi, P. Vetro, G. Soleimani Rad, Coupled fixed point results for T-contractions on cone metric spaces with applications, Math. Notes. 98 (1) (2015), 158-167.

[6] H. Rahimi, S. Radenovic, G. Soleimani Rad, Cone metric type space and new coupled fixed point theorems, J. Nonlinear. Anal. Optimization (JNAO). 6 (1) (2015), 1-9.

[7] S. Sedghi, I. Altun, N. Shobe, M. Salahshour, Some properties of S-metric space and fixed point results, Kyung pook Math. J. 54 (2014), 113-122.

[8] S. Sedghi, A. Gholidahneh, T. Dosenovic, J. Esfahani, S. Radenovic, Common fixed point of four maps in $S_b$-metric spaces, J. Linear. Topol. Algebra. 5 (2) (2016), 93-104.

[9] S. Sedghi, A. Gholidahneh, K. P. R. Rao, Common fixed point of two R- weakly commuting mappings in $S_b$-metric spaces, Mathematical Science letters (to appear).

[10] S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorem in S-metric spaces, Mat. Vesnik, 64 (2012), 258-266.

[11] S. Sedghi, N. Shobe, T. Dosenovic, Fixed point results in S-metric spaces, Nonlinear Funct. Anal. Appl. 20 (1) (2015), 55-67.