Various types of fixed-point theorems on S-metric spaces

Nihal Taş

Öz


Recently, some generalized metric spaces have been studied to obtain new fixed-point theorems. For example, the notion of S-metric space was introduced for this purpose. In this study, some fixed-point results are proved using different contractive conditions on S-metric spaces. Various techniques such as Hard-Rogers type contraction, Khan type contraction, Meir-Keeler-Khan type contraction are used in our theorems to be proved. These fixed-point results extend some known fixed-point theorems on S-metric spaces. Also, to illustrate obtained theoretical results, some examples are given using an S-metric which is not generated by any metric. As an application, a new fixed-circle result is presented using modified C-Khan type contraction on S-metric spaces. 


Tam Metin:

PDF

Referanslar


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

Hardy, G.E. and Rogers, T.D., A generalization of a fixed point theorem of Reich, Can. Math. Bull., 16, 201-206, (1973).

Kumari, P.S. and Panthi, D., Connecting various types of cyclic contractions and contractive self-mappings with Hardy-Rogers self-mappings, Fixed Point Theory Appl., 1, 15, (2016).

Fisher, B., On a theorem of Khan, Riv. Math. Univ. Parma., 4, 135-137, (1978).

Meir, A. and Keeler, E., A theorem on contraction mapping, J. Math. Anal. Appl., 28, 326-329, (1969).

Kumar, M. and Aracı, S., -Meir-Keeler-Khan type fixed point theorem in partial metric spaces, Bol. Soc. Paran. Mat., 36(4), 149-157, (2018).

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

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

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

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

Özgür, N.Y. and Taş, N., Some fixed point theorems on S-metric spaces, Mat. Vesnik, 69(1), 39-52, (2017).

Özgür, N.Y. and Taş, N., 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.

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

Özgür, N.Y. and Taş, N., Some fixed-circle theorems on metric spaces, Bull. Malays. Math. Sci. Soc., (2017). https://doi.org/10.1007/s40840-017-0555-z

Özgür, N.Y. and Taş, N., Some fixed-circle theorems on S-metric spaces with a geometric viewpoint, arXiv:1704.08838 [math.MG].

Özgür, N.Y., Taş, N. and Çelik, U., New fixed-circle results on S-metric spaces, Bull. Math. Anal. Appl., 9(2), 10-23, (2017).

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

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

Souayah, N., A fixed point in partial Sb-metric spaces, An. Ştiinţ. Univ. "Ovidius'' Constanţa Ser. Mat., 24(3), 351-362, (2016).


Refback'ler

  • Şu halde refbacks yoktur.


Telif Hakkı (c) 2018 Nihal TAŞ

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.