Öz
Geometric approaches are important for the study of some real-life problems. In metric fixed point theory, a recent problem called fixed-figure problem is the investigation of the existence of self-mapping which remain invariant at each points of a certain geometric figure (e.g. a circle, an ellipse and a Cassini curve) in the space. This problem is well studied in the domain of the extension of this line of research in the context of fixed circle, fixed disc, fixed ellipse, fixed Cassini curve and so on. In this paper, we introduce the concept of a Suzuki type $\mathcal{Z}_c$-contraction. We deal with the fixed-figure problem by means of the notions of a $\mathcal{Z}_c$-contraction and a Suzuki type $\mathcal{Z}_c$-contraction. We derive new fixed-figure results for the fixed ellipse and fixed Cassini curve cases by means of these notions. Also fixed disc and fixed circle results given for Suzuki type $\mathcal{Z}_c$-contraction. There are couple of illustration related to the obtained theoretical results.
Anahtar Kelimeler
Suzuki type $\mathcal{Z}_{c}$-contraction fixed disc fixed circle fixed ellipse fixed Cassini curve
Kaynakça
- [1] B. Angelov and I. M. Mladenov, On the geometry of red blood cell, in: Proceedings of the International Conference on Geometry, Integrability and Quantization. Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 27-46, 2000.
- [2] R.K. Bisht and N. Özgür, Geometric properties of discontinuous fixed point set of $(\epsilon -\delta)$ contractions and applications to neural networks, Aequationes Math. 94 (5), 847-863, 2020.
- [3] R.K. Bisht and N. Özgür, Discontinuous convex contractions and their applications in neural networks, Comput. Appl. Math. 40 (1), Paper No. 11, 11 pp, 2021.
- [4] A.P. Farajzadeh, M. Delfani and Y.H. Wang, Existence and uniqueness of fixed points of generalized F-contraction mappings, J. Math. (2021), Art. ID 6687238, 9 pp.
- [5] D. Gopal, J. Martínez-Moreno and N. Özgür, On fixed figure problems in fuzzy metric spaces, Kybernetika 59 (1), 110-129, 2023.
- [6] N. Guberman, On complex valued convolutional neural networks, arXiv:1602.09046 [cs.NE], 2016.
- [7] R. Hosseinzadeh, I. Sharifi and A. Taghavi, Maps completely preserving fixed points and maps completely preserving kernel of operators, Anal. Math. 44 (4), 451459, 2018.
- [8] M. Jleli, S. Bessem and C. Vetro, Fixed point theory in partial metric spaces via $\varphi $-fixed point’s concept in metric spaces, J. Inequal. Appl. 2014, 1-9, 2014.
- [9] E. Karapınar, Fixed points results via simulation functions, Filomat, 30 (8), 2343- 2350, 2016.
- [10] F. Khojasteh, S. Shukla and S. Radenovic, A new approach to the study of fixed point theory for simulation functions, Filomat, 29 (6), 1189-1194, 2015.
- [11] P. Kumam, D. Gopal and L. Budhiyi, A new fixed point theorem under Suzuki type $\mathcal{Z}$-contraction mappings, J. Math. Anal. 8 (1), 113-119, 2017.
- [12] N. Özgür, Fixed-disc results via simulation functions, Turkish J. Math. 43 (6), 2794- 2805, 2019.
- [13] N.Y. Özgür and N. Tas, Some fixed-circle theorems on metric spaces, Bull. Malays. Math. Sci. Soc. 42 (4), 1433-1449, 2019.
- [14] N. Özgür and N. Tas, On the geometry of $\varphi $-fixed points, in: Conference Proceedings of Science and Technology, 4 (2), 226-231, 2021.
- [15] N. Özgür and N. Tas, Geometric properties of fixed points and simulation functions, arXiv:2102.05417 [math.MG], 2021.
- [16] N. Özgür and N. Tas, $\varphi $-fixed points of self-mappings on metric spaces with a geometric viewpoint, arXiv:2107.11199 [math.GN], 2021.
- [17] N. Özgür, N. Tas and J.F. Peters, New complex-valued activation functions, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 10 (1), 66-72, 2020.
- [18] H.N. Saleh, M. Imdad and E. Karapınar, A study of common fixed points that belong to zeros of a certain given function with applications, Nonlinear Anal. Model. Control 26 (5), 781-800, 2021.
- [19] S. Shukla, D. Gopal and W. Sintunavarat, A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy sets and systems 350, 85-94, 2018.
- [20] R.G. Singh and A.P. Singh, Multiple complex extreme learning machine using holomorphic mapping for prediction of wind power generation system, Int. J. Comput. Math. Sci. Appl. 123 (18), 24-33, 2015.
- [21] Wolfram Research, Inc., Mathematica, Version 12.0, Champaign, IL (2019).
- [22] Z. Wu, A fixed point theorem, intermediate value theorem, and nested interval property, Anal. Math. 45 (2), 443-447, 2019.
Öz
Kaynakça
- [1] B. Angelov and I. M. Mladenov, On the geometry of red blood cell, in: Proceedings of the International Conference on Geometry, Integrability and Quantization. Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 27-46, 2000.
- [2] R.K. Bisht and N. Özgür, Geometric properties of discontinuous fixed point set of $(\epsilon -\delta)$ contractions and applications to neural networks, Aequationes Math. 94 (5), 847-863, 2020.
- [3] R.K. Bisht and N. Özgür, Discontinuous convex contractions and their applications in neural networks, Comput. Appl. Math. 40 (1), Paper No. 11, 11 pp, 2021.
- [4] A.P. Farajzadeh, M. Delfani and Y.H. Wang, Existence and uniqueness of fixed points of generalized F-contraction mappings, J. Math. (2021), Art. ID 6687238, 9 pp.
- [5] D. Gopal, J. Martínez-Moreno and N. Özgür, On fixed figure problems in fuzzy metric spaces, Kybernetika 59 (1), 110-129, 2023.
- [6] N. Guberman, On complex valued convolutional neural networks, arXiv:1602.09046 [cs.NE], 2016.
- [7] R. Hosseinzadeh, I. Sharifi and A. Taghavi, Maps completely preserving fixed points and maps completely preserving kernel of operators, Anal. Math. 44 (4), 451459, 2018.
- [8] M. Jleli, S. Bessem and C. Vetro, Fixed point theory in partial metric spaces via $\varphi $-fixed point’s concept in metric spaces, J. Inequal. Appl. 2014, 1-9, 2014.
- [9] E. Karapınar, Fixed points results via simulation functions, Filomat, 30 (8), 2343- 2350, 2016.
- [10] F. Khojasteh, S. Shukla and S. Radenovic, A new approach to the study of fixed point theory for simulation functions, Filomat, 29 (6), 1189-1194, 2015.
- [11] P. Kumam, D. Gopal and L. Budhiyi, A new fixed point theorem under Suzuki type $\mathcal{Z}$-contraction mappings, J. Math. Anal. 8 (1), 113-119, 2017.
- [12] N. Özgür, Fixed-disc results via simulation functions, Turkish J. Math. 43 (6), 2794- 2805, 2019.
- [13] N.Y. Özgür and N. Tas, Some fixed-circle theorems on metric spaces, Bull. Malays. Math. Sci. Soc. 42 (4), 1433-1449, 2019.
- [14] N. Özgür and N. Tas, On the geometry of $\varphi $-fixed points, in: Conference Proceedings of Science and Technology, 4 (2), 226-231, 2021.
- [15] N. Özgür and N. Tas, Geometric properties of fixed points and simulation functions, arXiv:2102.05417 [math.MG], 2021.
- [16] N. Özgür and N. Tas, $\varphi $-fixed points of self-mappings on metric spaces with a geometric viewpoint, arXiv:2107.11199 [math.GN], 2021.
- [17] N. Özgür, N. Tas and J.F. Peters, New complex-valued activation functions, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 10 (1), 66-72, 2020.
- [18] H.N. Saleh, M. Imdad and E. Karapınar, A study of common fixed points that belong to zeros of a certain given function with applications, Nonlinear Anal. Model. Control 26 (5), 781-800, 2021.
- [19] S. Shukla, D. Gopal and W. Sintunavarat, A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy sets and systems 350, 85-94, 2018.
- [20] R.G. Singh and A.P. Singh, Multiple complex extreme learning machine using holomorphic mapping for prediction of wind power generation system, Int. J. Comput. Math. Sci. Appl. 123 (18), 24-33, 2015.
- [21] Wolfram Research, Inc., Mathematica, Version 12.0, Champaign, IL (2019).
- [22] Z. Wu, A fixed point theorem, intermediate value theorem, and nested interval property, Anal. Math. 45 (2), 443-447, 2019.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Erken Görünüm Tarihi | 15 Ağustos 2023 |
| Yayımlanma Tarihi | 23 Nisan 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 53 Sayı: 2 |