Öz
TThe work of non-Newtonian calculus was begun in 1972. This calculus provides a different area to the classical one. Non-Newtonian metric concept was defined in 2002 by Basar and Cakmak. Then Binbaşıoğlu et al. had given the metric spaces of non-Newtonian in 2016. Also, they started to the fixed-point theory by defining some topological properties in non-Newtonian metric spaces.
In this work, we give some fixed-point theorems and results for self-mappings satisfying certain conditions in the non-Newtonian metric spaces.
Anahtar Kelimeler
Fixed point Non-Newtonian metric space Contraction mapping Generalized contraction mapping
Kaynakça
- [1] Alar R., Yigit Dakmaz E., Sola Erduran F., Gezici A., On Soft Fuzzy Metric Spaces and Topological Structure, Journal of Advanced Studies in Topology, 9 (2018) 61-70.
- [2] Aslantas M., Some Best Proximity Point Results via a New Family of F-Contraction and an Application to Homotopy Theory, Journal of Fixed Point Theory and Applications, 23 (4) (2021).
- [3] Aslantas M., Sahin H., Sadullah U., Some Generalizations for Mixed Multivalued Mappings, Applied General Topology, 23 (1) (2022) 169-178.
- [4] Aslantas M., Sahin H., Turkoglu D., Some Caristi Type Fixed-Point Theorems, The Journal of Analysis, 29 (2021) 89-103.
- [5] Binbasioglu D., Demiriz S., Turkoglu D., Fixed-Points of non-Newtonian Metric Spaces, J. Fixed Point Theory Appl., 18 (2016) 213-224.
- [6] Cakmak A. F., Basar F., Some New Results on Sequence Spaces with respect to non-Newtonian Calculus, J. Inequal. Appl., 2012 (2012) 228.
- [7] Cevik C., Altun I., Sahin H., Ozeken C. C., Some Fixed-Point Theorems for Contractive Mapping in Ordered Vector Metric Spaces, Journal of Nonlinear Sciences and Applications, 10 (4) (2017) 1424.1432.
- [8] Choudhary B., Nanda S., Functional Analysis with Applications. Newyork: John Wiley and Sons, (1990).
- [9] Grossman M. and Katz R., Non-Newtonian Calculus, Lowell Technological Institute (1972).
- [10] He X., Song M. and Chen D., Common Fixed-Points for Weak Commutative Mappings on a Multiplicative Metric Space, Fixed Point Theory Appl., 2014 (2014) 48.
- [11] Sola Erduran F., Yigit Dakmaz E., Alar R., Gezici A., Soft Fuzzy Metric Spaces, General Letters in Mathematics, 3 (2017) 91-101.
- [12] Uzer A., Multiplicative Type Complex Calculus as an Alternative to the Classical Calculus, Comput. Math. Appl., 60 (2010) 2725-2737.
Öz
Kaynakça
- [1] Alar R., Yigit Dakmaz E., Sola Erduran F., Gezici A., On Soft Fuzzy Metric Spaces and Topological Structure, Journal of Advanced Studies in Topology, 9 (2018) 61-70.
- [2] Aslantas M., Some Best Proximity Point Results via a New Family of F-Contraction and an Application to Homotopy Theory, Journal of Fixed Point Theory and Applications, 23 (4) (2021).
- [3] Aslantas M., Sahin H., Sadullah U., Some Generalizations for Mixed Multivalued Mappings, Applied General Topology, 23 (1) (2022) 169-178.
- [4] Aslantas M., Sahin H., Turkoglu D., Some Caristi Type Fixed-Point Theorems, The Journal of Analysis, 29 (2021) 89-103.
- [5] Binbasioglu D., Demiriz S., Turkoglu D., Fixed-Points of non-Newtonian Metric Spaces, J. Fixed Point Theory Appl., 18 (2016) 213-224.
- [6] Cakmak A. F., Basar F., Some New Results on Sequence Spaces with respect to non-Newtonian Calculus, J. Inequal. Appl., 2012 (2012) 228.
- [7] Cevik C., Altun I., Sahin H., Ozeken C. C., Some Fixed-Point Theorems for Contractive Mapping in Ordered Vector Metric Spaces, Journal of Nonlinear Sciences and Applications, 10 (4) (2017) 1424.1432.
- [8] Choudhary B., Nanda S., Functional Analysis with Applications. Newyork: John Wiley and Sons, (1990).
- [9] Grossman M. and Katz R., Non-Newtonian Calculus, Lowell Technological Institute (1972).
- [10] He X., Song M. and Chen D., Common Fixed-Points for Weak Commutative Mappings on a Multiplicative Metric Space, Fixed Point Theory Appl., 2014 (2014) 48.
- [11] Sola Erduran F., Yigit Dakmaz E., Alar R., Gezici A., Soft Fuzzy Metric Spaces, General Letters in Mathematics, 3 (2017) 91-101.
- [12] Uzer A., Multiplicative Type Complex Calculus as an Alternative to the Classical Calculus, Comput. Math. Appl., 60 (2010) 2725-2737.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Natural Sciences |
| Yazarlar | |
| Yayımlanma Tarihi | 29 Haziran 2022 |
| Gönderilme Tarihi | 11 Ekim 2021 |
| Kabul Tarihi | 19 Nisan 2022 |
| Yayımlandığı Sayı | Yıl 2022 |