Araştırma Makalesi
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S-metrik uzaylar üzerinde sabit-nokta teoremlerinin çeşitli türleri

Yıl 2018, Cilt: 20 Sayı: 2, 211 - 223, 01.12.2018
https://doi.org/10.25092/baunfbed.426665

Öz

Son zamanlarda yeni sabit nokta teoremleri elde etmek için bazı genelleştirilmiş metrik uzaylar çalışılmaktadır. Örneğin, S-metrik uzay kavramı bu amaç için tanıtılmıştır. Bu çalışmada, S-metrik uzaylar üzerinde farklı daralma koşulları kullanılarak bazı sabit nokta sonuçları ispatlanmıştır. İspatlanan teoremlerde Hardy-Rogers tipinde daralma, Khan tipinde daralma, Meir-Keeler-Khan tipinde daralma gibi çeşitli teknikler kullanılmıştır. Bu sabit nokta sonuçları S-metrik uzaylar üzerindeki bazı bilinen sabit nokta sonuçlarını genellemektedir. Ayrıca, herhangi bir metrik tarafından üretilemeyen S-metrik örnekleri kullanılarak elde edilen teorik sonuçları gerçekleyecek bazı örnekler verilmiştir. S-metrik uzaylar üzerinde bir uygulama olarak değiştirilmiş C-Khan tipinde daralma kavramı kullanılarak yeni bir sabit çember sonucu verilmiştir.

Kaynakça

  • 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).

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

Yıl 2018, Cilt: 20 Sayı: 2, 211 - 223, 01.12.2018
https://doi.org/10.25092/baunfbed.426665

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. 

Kaynakça

  • 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).
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Nihal Taş Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2018
Gönderilme Tarihi 16 Şubat 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 20 Sayı: 2

Kaynak Göster

APA Taş, N. (2018). Various types of fixed-point theorems on S-metric spaces. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20(2), 211-223. https://doi.org/10.25092/baunfbed.426665
AMA Taş N. Various types of fixed-point theorems on S-metric spaces. BAUN Fen. Bil. Enst. Dergisi. Aralık 2018;20(2):211-223. doi:10.25092/baunfbed.426665
Chicago Taş, Nihal. “Various Types of Fixed-Point Theorems on S-Metric Spaces”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20, sy. 2 (Aralık 2018): 211-23. https://doi.org/10.25092/baunfbed.426665.
EndNote Taş N (01 Aralık 2018) Various types of fixed-point theorems on S-metric spaces. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 2 211–223.
IEEE N. Taş, “Various types of fixed-point theorems on S-metric spaces”, BAUN Fen. Bil. Enst. Dergisi, c. 20, sy. 2, ss. 211–223, 2018, doi: 10.25092/baunfbed.426665.
ISNAD Taş, Nihal. “Various Types of Fixed-Point Theorems on S-Metric Spaces”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20/2 (Aralık 2018), 211-223. https://doi.org/10.25092/baunfbed.426665.
JAMA Taş N. Various types of fixed-point theorems on S-metric spaces. BAUN Fen. Bil. Enst. Dergisi. 2018;20:211–223.
MLA Taş, Nihal. “Various Types of Fixed-Point Theorems on S-Metric Spaces”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 20, sy. 2, 2018, ss. 211-23, doi:10.25092/baunfbed.426665.
Vancouver Taş N. Various types of fixed-point theorems on S-metric spaces. BAUN Fen. Bil. Enst. Dergisi. 2018;20(2):211-23.