Document Type : Research Paper


1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Qaemshar Branch, Islamic Azad University, Qaemshar, Iran

3 Department of Mathematics, Babol Branch, Islamic Azad University, Babol, Iran

4 Faculty of Electrical Engineering, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina


In this paper, we prove a general fixed point theorem in $\textrm{S}$-metric spaces for maps satisfying an implicit relation on complete metric spaces. As applications, we get many analogues of fixed point theorems in metric spaces for $\textrm{S}$-metric spaces.


Main Subjects

[1] R. P. Agarwal, M. Meehan, D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, 2004.
[2] I. Altun, D. Turkoglu, Fixed point and homotopy result for mappings satisfying an implicit relation, Discuss. Math. Differ. Incl. Control Optim. 27 (2007), 349-363.
[3] I. Altun, H. A. Hancer, D. Turkoglu, A fixed point theorem for multi-maps satisfying an implicit relation on metrically convex metric spaces, Math. Commun. 11 (2006), 17-23.
[4] M. Imdad, S. Kumar, M. S. Khan, Remarks on some fixed point theorems satisfying implicit relations, Rad. Math. 11 (1) (2002), 135-143.
[5] M. Jovanovic, Z. Kadelburg, S. Radenovic, Common fixed point results in metric-type spaces, Fixed Point Theory Appl. 2010, 2010:978121.
[6] M. A. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. 2010, 2010:315398.
[7] M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal. 7 (9) (2010), 3123-3129.
[8] Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2) (2006), 289-297.
[9] V. Popa, A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation, Demonstratio Math. 33 (1) (2000), 159-164.
[10] V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32 (1) (1999), 157-163.
[11] S. Sharma, B. Desphande, On compatible mappings satisfying an implicit relation in common fixed point consideration, Tamkang J. Math. 33 (3) (2002), 245-252.
[12] S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorem in S-metric spaces, Mat. Vesnik. 64 (3) (2012), 258-266.
[13] S. Sedghi, N. Shobe, H. Zhou, A common fixed point theorem in D∗-metric spaces, Fixed Point Theory Appl. 2007, 2007:27906.