Araştırma Makalesi
BibTex RIS Kaynak Göster

S-metrik uzaylarda ikili tipinde daralmalar yardımıyla yeni sabit-disk sonuçları

Yıl 2022, , 408 - 416, 05.01.2022
https://doi.org/10.25092/baunfbed.995307

Öz

Banach daralma koşulunu sağlamayan ve bir tek sabit noktası ya da birden fazla sabit noktası olan fonksiyon örnekleri mevcuttur. Bu durumda, metrik sabit-nokta teorisi bazı teknikler kullanılarak kapsamlı olarak genelleştirilmektedir. Bu tekniklerden biri Jaggi tipinde daralma koşulu, Dass-Gupta tipinde daralma koşulu gibi kullanılan daralma koşulunun genelleştirilmesidir. Diğer bir teknik ise b-metrik uzay, S-metrik uzay gibi kullanılan metrik uzayın genelleştirilmesidir. Son teknik ise sabit çember, sabit disk gibi verilen bir fonksiyonun sabit nokta kümesinin geometrik özelliklerinin incelenmesidir. Bu amaç için, “sabit-çember problemi” metrik sabit-nokta teorisinin geometrik bir genellemesi olarak çeşitli tekniklerle çalışılmaktadır. Bu problem ayrıca “sabit-figür problemi” olarak da düşünülebilir. Bu son problemlere bazı çözümler hem metrik uzaylar üzerinde hem de genelleştirilmiş metrik uzaylar üzerinde farklı daralmalar kullanılarak elde edilmiştir. Bu makalenin ana amacı S-metrik uzaylar üzerinde bazı sabit-disk teoremleri ispatlamaktır. Bunun için, Bunun için bilinen bazı daralma koşullarını modifiye edeceğiz. Ayrıca elde edilen bu yeni teoremleri bazı gerçekleyici örnekler ile destekleyeceğiz.

Kaynakça

  • Banach, S., Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fundamenta Mathematicae, 2, 133–181, (1922).
  • Sedghi, S., Shobe, N. and Aliouche, A., A generalization of fixed point theorems in S-metric spaces, Matematički Vesnik, 64(3), 258–266, (2012).
  • Bakhtin, I. A., The contraction principle in quasimetric spaces, Func. An. Ulian. Gos. Ped. Ins., 30, 26–37, (1989).
  • Sedghi, S. and Dung, N. V., Fixed point theorems on S-metric spaces, Matematički Vesnik, 66(1), 113–124, (2014).
  • Özgür, N. Y. and Taş, N., Some fixed-circle theorems on metric spaces, Bulletin of the Malaysian Mathematical Sciences Society, 42(4), 1433–1449, (2019).
  • Mlaiki, N., Çelik, U., Taş, N., Özgür, N. Y. and Mukheimer, A., Wardowski type contractions and the fixed-circle problem on S-metric spaces, Journal of Mathematics, Art. ID 9127486, 9 pp, (2018).
  • Özgür, N. Y., Taş, N. and Çelik, U., New fixed-circle results on S-metric spaces. Bulletin of Mathematical Analysis and Applications, 9(2), 10–23, (2017).
  • Özgür, N. Y. and Taş, N., Fixed-circle problem on S-metric spaces with a geometric viewpoint, Facta Universitatis. Series: Mathematics and Informatics, 34(3), 459–472, (2019).
  • Taş, N. and Özgür, N., On the geometry of fixed points for self-mappings on S-metric spaces, Communications Faculty of Sciences University of Ankara Series A1-Mathematics and Statistics, 69(2), 190–198, (2020).
  • Özgür, N. Y. and Taş, N., Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25), Mathematical Sciences, 11(1), 7–16, (2017).
  • Wolfram Research, Inc., Mathematica, Version 12.0, Champaign, IL (2019).
  • Chen, C. M., Joonaghany, G. H., Karapınar, E. and Khojasteh, F., On bilateral contractions, Mathematics, 7, 38, (2019).
  • Taş, N., Bilateral-type solutions to the fixed-circle problem with rectified linear units application, Turkish Journal of Mathematics, 44(4), 1330–1344, (2020).
  • Özgür, N. Y. and Taş, N., Geometric properties of fixed points and simulation functions, arXiv:2102.05417, (2021).

New fixed-disc results via bilateral type contractions on S-metric spaces

Yıl 2022, , 408 - 416, 05.01.2022
https://doi.org/10.25092/baunfbed.995307

Öz

There are some examples of self-mappings which does not satisfy the Banach contractive condition and have a unique fixed point or more than one fixed point. In this case, metric fixed-point theory has been extensively generalized using some techniques. One of these techniques is to generalize the used contractive conditions such as the Jaggi type contractive condition, the Dass-Gupta type contractive condition etc. Another technique is to generalize the used metric spaces such as a b-metric space, an S-metric space etc. The last technique is to investigate geometric properties of the fixed-point set of a given self-mapping such as fixed circle, fixed disc etc. For this purpose, “fixed-circle problem” has been studied with various techniques as a geometrical generalization of the metric fixed-point theory. This problem was also considered as “fixed-figure problem”. Some solutions to these recent problems were obtained using different contractions both a metric space and a generalized metric space. The main purpose of this paper is to prove some fixed-disc theorems on an S-metric space. To do this, we modify the known contractive conditions. Also, the obtained new theorems are supported by some illustrative examples.

Kaynakça

  • Banach, S., Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fundamenta Mathematicae, 2, 133–181, (1922).
  • Sedghi, S., Shobe, N. and Aliouche, A., A generalization of fixed point theorems in S-metric spaces, Matematički Vesnik, 64(3), 258–266, (2012).
  • Bakhtin, I. A., The contraction principle in quasimetric spaces, Func. An. Ulian. Gos. Ped. Ins., 30, 26–37, (1989).
  • Sedghi, S. and Dung, N. V., Fixed point theorems on S-metric spaces, Matematički Vesnik, 66(1), 113–124, (2014).
  • Özgür, N. Y. and Taş, N., Some fixed-circle theorems on metric spaces, Bulletin of the Malaysian Mathematical Sciences Society, 42(4), 1433–1449, (2019).
  • Mlaiki, N., Çelik, U., Taş, N., Özgür, N. Y. and Mukheimer, A., Wardowski type contractions and the fixed-circle problem on S-metric spaces, Journal of Mathematics, Art. ID 9127486, 9 pp, (2018).
  • Özgür, N. Y., Taş, N. and Çelik, U., New fixed-circle results on S-metric spaces. Bulletin of Mathematical Analysis and Applications, 9(2), 10–23, (2017).
  • Özgür, N. Y. and Taş, N., Fixed-circle problem on S-metric spaces with a geometric viewpoint, Facta Universitatis. Series: Mathematics and Informatics, 34(3), 459–472, (2019).
  • Taş, N. and Özgür, N., On the geometry of fixed points for self-mappings on S-metric spaces, Communications Faculty of Sciences University of Ankara Series A1-Mathematics and Statistics, 69(2), 190–198, (2020).
  • Özgür, N. Y. and Taş, N., Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25), Mathematical Sciences, 11(1), 7–16, (2017).
  • Wolfram Research, Inc., Mathematica, Version 12.0, Champaign, IL (2019).
  • Chen, C. M., Joonaghany, G. H., Karapınar, E. and Khojasteh, F., On bilateral contractions, Mathematics, 7, 38, (2019).
  • Taş, N., Bilateral-type solutions to the fixed-circle problem with rectified linear units application, Turkish Journal of Mathematics, 44(4), 1330–1344, (2020).
  • Özgür, N. Y. and Taş, N., Geometric properties of fixed points and simulation functions, arXiv:2102.05417, (2021).
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Nihal Taş 0000-0002-4535-4019

Yayımlanma Tarihi 5 Ocak 2022
Gönderilme Tarihi 14 Eylül 2021
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Taş, N. (2022). New fixed-disc results via bilateral type contractions on S-metric spaces. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 24(1), 408-416. https://doi.org/10.25092/baunfbed.995307
AMA Taş N. New fixed-disc results via bilateral type contractions on S-metric spaces. BAUN Fen. Bil. Enst. Dergisi. Ocak 2022;24(1):408-416. doi:10.25092/baunfbed.995307
Chicago Taş, Nihal. “New Fixed-Disc Results via Bilateral Type Contractions on S-Metric Spaces”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24, sy. 1 (Ocak 2022): 408-16. https://doi.org/10.25092/baunfbed.995307.
EndNote Taş N (01 Ocak 2022) New fixed-disc results via bilateral type contractions on S-metric spaces. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24 1 408–416.
IEEE N. Taş, “New fixed-disc results via bilateral type contractions on S-metric spaces”, BAUN Fen. Bil. Enst. Dergisi, c. 24, sy. 1, ss. 408–416, 2022, doi: 10.25092/baunfbed.995307.
ISNAD Taş, Nihal. “New Fixed-Disc Results via Bilateral Type Contractions on S-Metric Spaces”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24/1 (Ocak 2022), 408-416. https://doi.org/10.25092/baunfbed.995307.
JAMA Taş N. New fixed-disc results via bilateral type contractions on S-metric spaces. BAUN Fen. Bil. Enst. Dergisi. 2022;24:408–416.
MLA Taş, Nihal. “New Fixed-Disc Results via Bilateral Type Contractions on S-Metric Spaces”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 24, sy. 1, 2022, ss. 408-16, doi:10.25092/baunfbed.995307.
Vancouver Taş N. New fixed-disc results via bilateral type contractions on S-metric spaces. BAUN Fen. Bil. Enst. Dergisi. 2022;24(1):408-16.