Document Type: Special Issue on Fixed Point Theory


Department of Mathematics, Bali kesir University, 10145 Balikesir, Turkey


In this paper, the notions of a Suzuki-Berinde type $F_{S}$-contraction and a Suzuki-Berinde type $F_{C}^{S}$-contraction are introduced on a $S$-metric space. Using these new notions, a fixed-point theorem is proved on a complete $S$-metric space and a fixed-circle theorem is established on a $S$-metric space. Some examples are given to support the obtained results.


Main Subjects

[1] I. A. Bakhtin, The contraction principle in quasimetric spaces, Func. An. Ulian. Gos. Ped. Ins. 30 (1989), 26-37.

[2] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fund. Math. 2 (1922), 133-181.

[3] V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear. Anal. Forum. 9 (2004), 43-53.

[4] V. Berinde, General constructive fixed point theorem for Ciric-type almost contractions in metric spaces, Carpath. J. Math. 24 (2008), 10-19.

[5] S. Chaipornjareansri, Fixed point theorems for Fw -contractions in complete S-metric spaces, Thai. J. Math. (2016), 98-109.

[6] A. Gupta, Cyclic contraction on S-metric space, Int. J. Anal. Appl. 3 (2) (2013), 119-130.

[7] N. T. Hieu, N. T. Ly, N. V. Dung, A generalization of Ciric quasi-contractions for maps on S-metric spaces, Thai. J. Math. 13 (2) (2015), 369-380.

[8] N. Hussain, J. Ahmad, New Suzuki-Berinde type fixed point results, Carpath. J. Math. 33 (1) (2017), 59-72.

[9] N. Mlaiki, α-ψ-contractive mapping on S-metric space, Math. Sci. Lett. 4 (1) (2015), 9-12.

[10] N. Mlaiki, Common fixed points in complex S-metric space, Adv. Fixed. Point. Theory. 4 (4) (2014), 509-524.

[11] N. Y. Ozgur, N. Tas, Fixed-circle problem on S-metric spaces with a geometric viewpoint, arXiv:1704.08838 [math.MG].

[12] N. Y. Ozgur, N. Tas, Some fixed-circle theorems and discontinuity at fixed circle, AIP Conference Proceedings (2018), 1926-020048.

[13] N. Y. Ozgur, N. Tas, Some fixed-circle theorems on metric spaces, Bull. Malays. Math. Sci. Soc. (2017),

[14] N. Y. Ozgur, N. Tas, Some fixed-point theorems on S-metric spaces, Mat. Vesnik. 69 (1) (2017), 39-52.

[15] N. Y. Ozgur, N. Tas, Some generalizations of fixed point theorems on S-metric spaces, Essays in Mathematics and Its Applications in Honor of Vladimir Arnold, New York, Springer, 2016.

[16] N. Y. Ozgur, N. Tas, Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25), Math. Sci. 11 (1) (2017), 7-16.

[17] N. Y.Ozgur, N. Tas, U. Celik, New xed-circle results on S-metric spaces, Bull. Math. Anal. Appl. 9 (2) (2017), 10-23.

[18] H. Piri, P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl. (2014), 2014:210.

[19] K. P. R. Rao, G. N. V. Kishore, S. Sadik, Unique common coupled fixed point theorem for four maps in Sb-metric spaces, J. Linear. Topological. Algebra. 6 (1) (2017), 29-43.

[20] N. A. Secelean, Iterated function systems consisting of F -contractions, Fixed Point Theory  Appl. (2013), 2013:277.

[21] S. Sedghi, N. V. Dung, Fixed point theorems on S-metric spaces, Mat. Vesnik. 66 (1) (2014), 113-124.

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

[23] S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik. 64 (3) (2012), 258-266.

[24] N. Souayah, A fixed point in partial Sb-metric spaces, An. Stiint. Univ. “Ovidius” Constan¸ta Ser. Mat. 24 (3) (2016), 351-362.

[25] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869.

[26] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. (2012), 2012:94.