In this paper, we mention new results to the fixed-figure problem on Sb- metric spaces. Especially, we emphasize Cassini curve and Appolonius circle. To do this, first of all we give the new notions of Moradi-type Cu1u2- Sb-contraction, Geraghty-type Cu1u2- Sb-contraction, Skof-type Cu1u2- Sb-contraction, Moradi-type Au1u2- Sb-contraction, Geraghty-type Au1u2- Sb-contraction, Skoftype Au1u2- Sb-contraction. With the help of these notions, we obtain some fixed-Cassini curve and fixed-Apollonius circle theorems on Sb- metric spaces.
Banach S., Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fundamenta Mathematicae, 2, 133-181, (1922).
Babu A. S., Dosenovic T., Ali M. M., Radenovic A., Rao K. P. R. Some Presic type results in b-dislocated metric spaces, Contructive Mathematical Analysis, 2 ,1, 40-48, (2019).
Karapınar E., A short survey on the recent fized point results on b-metric spaces, Contructive Mathematical Analysis, 1, 1, 15-44, (2018).
Nazam M., Arshad M. Park C., Acar Ö., Yun S., Anastassiou G. A., On solution of a system of differntial equations via fixed point theorem, Journal of Applied Analysis and Computation, 27, 3, 417-426, (2019).
Sedghi S., Gholidahneh A., Dosenovic T., Esfahani J., Radenovic S. Common fixed point of four maps in -metric spaces, Journal of Linear and Topological Algebra, 5, 2, 93-104, (2016).
Taş N., Özgür N. A new generalization of Rhoades’ condition, International Journal of Optimization and Control: Theories & Applications, 12, 2, 169-183, (2022).
Özgür N. Y., Taş N. Some fixed-circle theorems on metric spaces, Bulletin of The Malaysian Mathematical Sciences Society, 42, 4, 1433-1449, (2019).
Mlaiki N., Özgür N., Taş N. New-fixed circle results related to -contractive and -expanding mappings on metric spaces, arXiv:2101.10770.
Özgür N. Y., Taş N., Some fixed circle theorems and discontinuity at fixed circle, AIP Conference Proceeding 1926, 020048, (2018).
Özgür N. Y., Taş N. Generalizations of Metric Spaces: From the Fixed-Point Theory to the fixed-circle Theory, Applications of Nonlinear Analysis Springer Optimization and Its Applications, 134, Springer, Cham, 847-895, (2018).
Özgür N. Y. Fixed-disc results via simulation functions, Turkish Journal Mathematics, 43, 6, 2794-2805, (2019).
Pant R. P., Özgür N. Y., Taş N. Discontinuity at fixed points with applications, Bulletin of The Malaysian Mathematical Sciences Society-Simon Stevin, 26, 571-589, (2019).
Pant R. P., Özgür N. Y., Taş N. On discontinuity problem at fixed point, Bulletin of The Malaysian Mathematical Sciences Society, 43, 499-517, (2020).
Pant R. P., Özgür N. Y., Taş N., Pant A., Joshi M. C. New results on discontinuity at fixed point, Journal of Fixed Point Theory Applications, 22, 39, (2020).
Taş N. Bilateral-type solutions to the fixed-circle problem with rectified linear units application, Turkish Journal of Mathematics, 44, 4, 133330-1344, (2020).
Özgür N. Y., Taş N. Geometric properties of fixed points and simulation functions, arXiv:2102.05417.
Erçınar G. Z., Some Geometric properties of fixed-points, Doktora Tezi, Osmangazi Üniversitesi, Fen Bilimleri Enstitüsü, Eskişehir, (2020).
Joshi M., Tomar A., Padaliya S. K. Fixed point to fixed ellipse in metric spaces and discontinuous activation function, Applied Mathematics E-Notes, 21, 225-237, (2021).
Taş N., A contribution to the fixed-disc results on S-metric spaces, 7th Ifs And Contemporary Mathematics Conference, May, 25-29, Turkey, 172-176, (2021).
Özgür N. Y., Taş N. New fixed-figure results on metric spaces, Fixed point theory and fractional calculus—recent advances and applications, Forum Interdiscip. Math., Springer, Singapore, 33–62, (2022).
Aytimur H., Taş N. A., geometric interpretation to fixed-point theory on -metric spaces, Electronic Journal of Mathematical Analysis and Applications., 10, 2, 95–104, (2022).
Aytimur H., Güvenç Ş., Taş N., New Fixed-Figure Results with the Notion of k-Ellipse, Mathematica Moravica, 27, 1, 37–52, (2023).
Taş N., Ayoob I., Mlaiki N., Some common fixed-point and fixed-figure results with a function family on -metric spaces, AIMS Mathematics, 8, 6, 13050-13065, (2023).
Bakhtin I. A. The contraction mapping principle in quasimetric spaces, Functional Analysis Uni-anowsk Gos. Ped. Institute, 30, 26-37, (1989).
Sedghi S., Shobe N., Aliouche A. A generalization of fixed point theorems in S-metric spaces, Matematicki Vesnik, 64, 3, 258-266, (2012).
Taş N., Özgür N. New generalized fixed point results on -metric spaces, Konuralp Journal of Mathematics, 9, 1, 24-32, (2021).
Moradi S. Fixed point of single-valued cyclic weak -contraction mappings, Filomat, 28, 1747-1752, (2014).
Geraghty M. A. On contractive mappings, Proceeding of the American Mathematical Society, 40, 604-608, (1973).
Skof F. Theoremi di punto fisso per applicazioni negli spazi metrici, Atti Accademia Scienze Torino Classe Fisiche Matematiche Naturali, 111, 323-329, (1977).
Özgür N. Y., Taş N. Some new contractive mappings on -metric spaces and their relationships with the mapping (S25), Mathematical Sciences, 11, 1, 7-16, (2017).
Bu çalışmada, Sb - metrik uzaylarda sabit figüre problemleri için yeni çözümlerden bahsedilecektir. Özellikle, Cassini Eğrisi ve Apoollonius çemberi üzerinde durulacaktır. Bunun için ilk olarak Moradi tipinde Cu1u2-Sb -daralma, Geraghty tipinde Cu1u2-Sb -daralma, Skof tipinde Cu1u2-Sb -daralma, Moradi tipinde Au1u2-Sb -daralma, Geraghty tipinde Au1u2-Sb -daralma, Skof tipinde Au1u2-Sb -daralma kavramları verilecektir. Bu kavramlar yardımı ile - metrik uzaylar üzerinde sabit Cassini eğrisi ve sabit Apollonius çemberi teoremleri elde edilecektir.
Banach S., Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fundamenta Mathematicae, 2, 133-181, (1922).
Babu A. S., Dosenovic T., Ali M. M., Radenovic A., Rao K. P. R. Some Presic type results in b-dislocated metric spaces, Contructive Mathematical Analysis, 2 ,1, 40-48, (2019).
Karapınar E., A short survey on the recent fized point results on b-metric spaces, Contructive Mathematical Analysis, 1, 1, 15-44, (2018).
Nazam M., Arshad M. Park C., Acar Ö., Yun S., Anastassiou G. A., On solution of a system of differntial equations via fixed point theorem, Journal of Applied Analysis and Computation, 27, 3, 417-426, (2019).
Sedghi S., Gholidahneh A., Dosenovic T., Esfahani J., Radenovic S. Common fixed point of four maps in -metric spaces, Journal of Linear and Topological Algebra, 5, 2, 93-104, (2016).
Taş N., Özgür N. A new generalization of Rhoades’ condition, International Journal of Optimization and Control: Theories & Applications, 12, 2, 169-183, (2022).
Özgür N. Y., Taş N. Some fixed-circle theorems on metric spaces, Bulletin of The Malaysian Mathematical Sciences Society, 42, 4, 1433-1449, (2019).
Mlaiki N., Özgür N., Taş N. New-fixed circle results related to -contractive and -expanding mappings on metric spaces, arXiv:2101.10770.
Özgür N. Y., Taş N., Some fixed circle theorems and discontinuity at fixed circle, AIP Conference Proceeding 1926, 020048, (2018).
Özgür N. Y., Taş N. Generalizations of Metric Spaces: From the Fixed-Point Theory to the fixed-circle Theory, Applications of Nonlinear Analysis Springer Optimization and Its Applications, 134, Springer, Cham, 847-895, (2018).
Özgür N. Y. Fixed-disc results via simulation functions, Turkish Journal Mathematics, 43, 6, 2794-2805, (2019).
Pant R. P., Özgür N. Y., Taş N. Discontinuity at fixed points with applications, Bulletin of The Malaysian Mathematical Sciences Society-Simon Stevin, 26, 571-589, (2019).
Pant R. P., Özgür N. Y., Taş N. On discontinuity problem at fixed point, Bulletin of The Malaysian Mathematical Sciences Society, 43, 499-517, (2020).
Pant R. P., Özgür N. Y., Taş N., Pant A., Joshi M. C. New results on discontinuity at fixed point, Journal of Fixed Point Theory Applications, 22, 39, (2020).
Taş N. Bilateral-type solutions to the fixed-circle problem with rectified linear units application, Turkish Journal of Mathematics, 44, 4, 133330-1344, (2020).
Özgür N. Y., Taş N. Geometric properties of fixed points and simulation functions, arXiv:2102.05417.
Erçınar G. Z., Some Geometric properties of fixed-points, Doktora Tezi, Osmangazi Üniversitesi, Fen Bilimleri Enstitüsü, Eskişehir, (2020).
Joshi M., Tomar A., Padaliya S. K. Fixed point to fixed ellipse in metric spaces and discontinuous activation function, Applied Mathematics E-Notes, 21, 225-237, (2021).
Taş N., A contribution to the fixed-disc results on S-metric spaces, 7th Ifs And Contemporary Mathematics Conference, May, 25-29, Turkey, 172-176, (2021).
Özgür N. Y., Taş N. New fixed-figure results on metric spaces, Fixed point theory and fractional calculus—recent advances and applications, Forum Interdiscip. Math., Springer, Singapore, 33–62, (2022).
Aytimur H., Taş N. A., geometric interpretation to fixed-point theory on -metric spaces, Electronic Journal of Mathematical Analysis and Applications., 10, 2, 95–104, (2022).
Aytimur H., Güvenç Ş., Taş N., New Fixed-Figure Results with the Notion of k-Ellipse, Mathematica Moravica, 27, 1, 37–52, (2023).
Taş N., Ayoob I., Mlaiki N., Some common fixed-point and fixed-figure results with a function family on -metric spaces, AIMS Mathematics, 8, 6, 13050-13065, (2023).
Bakhtin I. A. The contraction mapping principle in quasimetric spaces, Functional Analysis Uni-anowsk Gos. Ped. Institute, 30, 26-37, (1989).
Sedghi S., Shobe N., Aliouche A. A generalization of fixed point theorems in S-metric spaces, Matematicki Vesnik, 64, 3, 258-266, (2012).
Taş N., Özgür N. New generalized fixed point results on -metric spaces, Konuralp Journal of Mathematics, 9, 1, 24-32, (2021).
Moradi S. Fixed point of single-valued cyclic weak -contraction mappings, Filomat, 28, 1747-1752, (2014).
Geraghty M. A. On contractive mappings, Proceeding of the American Mathematical Society, 40, 604-608, (1973).
Skof F. Theoremi di punto fisso per applicazioni negli spazi metrici, Atti Accademia Scienze Torino Classe Fisiche Matematiche Naturali, 111, 323-329, (1977).
Özgür N. Y., Taş N. Some new contractive mappings on -metric spaces and their relationships with the mapping (S25), Mathematical Sciences, 11, 1, 7-16, (2017).
Aytimur, H. (2023). Sb-Metrik Uzaylarda Bazı Sabit Eğriler Üzerine. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 25(2), 650-660. https://doi.org/10.25092/baunfbed.1280244
AMA
Aytimur H. Sb-Metrik Uzaylarda Bazı Sabit Eğriler Üzerine. BAUN Fen. Bil. Enst. Dergisi. Temmuz 2023;25(2):650-660. doi:10.25092/baunfbed.1280244
Chicago
Aytimur, Hülya. “Sb-Metrik Uzaylarda Bazı Sabit Eğriler Üzerine”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 25, sy. 2 (Temmuz 2023): 650-60. https://doi.org/10.25092/baunfbed.1280244.
EndNote
Aytimur H (01 Temmuz 2023) Sb-Metrik Uzaylarda Bazı Sabit Eğriler Üzerine. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 25 2 650–660.
IEEE
H. Aytimur, “Sb-Metrik Uzaylarda Bazı Sabit Eğriler Üzerine”, BAUN Fen. Bil. Enst. Dergisi, c. 25, sy. 2, ss. 650–660, 2023, doi: 10.25092/baunfbed.1280244.
ISNAD
Aytimur, Hülya. “Sb-Metrik Uzaylarda Bazı Sabit Eğriler Üzerine”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 25/2 (Temmuz 2023), 650-660. https://doi.org/10.25092/baunfbed.1280244.
JAMA
Aytimur H. Sb-Metrik Uzaylarda Bazı Sabit Eğriler Üzerine. BAUN Fen. Bil. Enst. Dergisi. 2023;25:650–660.
MLA
Aytimur, Hülya. “Sb-Metrik Uzaylarda Bazı Sabit Eğriler Üzerine”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 25, sy. 2, 2023, ss. 650-6, doi:10.25092/baunfbed.1280244.
Vancouver
Aytimur H. Sb-Metrik Uzaylarda Bazı Sabit Eğriler Üzerine. BAUN Fen. Bil. Enst. Dergisi. 2023;25(2):650-6.