Öz
In this work, we focus on investigating statistical convergence in function spaces equipped with semi-uniform convergence topologies. We provide a comparative analysis of pointwise and uniform statistical convergence under these topological structures and investigate the conditions that allow transitions between these types of convergence.
Anahtar Kelimeler
Statistical convergence Topology of semi-uniform convergence function spaces
Kaynakça
- [1] Kelley, J. L. (1975). General Topology, Springer, New York–Berlin.
- [2] Bourbaki, N. (1989). General Topology, Springer, Berlin.
- [3] Husek, M. (1964). Generalized proximity and uniform spaces I, Comment. Math. Univ. Carolinae, 5, 247–266.
- [4] Husek, M. (1965). Generalized proximity and uniform spaces II, Comment. Math. Univ. Carolinae, 6, 119–139.
- [5] Čech, E. (1966). Topological Spaces (revised by Z. Frolík and M. Katětov), Academia Publishing House of the Czechoslovak Academy of Sciences, Prague.
- [6] Page, W. (1989). Topological Uniform Structures, Dover Publications Inc., New York.
- [7] Fast, H. (1951). Sur la convergence statistique, Colloq. Math. 2, 241–244.
- [8] Steinhaus, H. (1951). Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2, 73–74.
- [9] Zygmund, A. (1979). Trigonometric Series (2nd ed.), Cambridge University Press, Cambridge.
- [10] Balcerzak, M., Dems, K., Komisarski, A. (2007). Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328(1), 715–729. DOI: 10.1016/j.jmaa.2006.05.040
- [11] Caserta, A., Maio, G. Di., Kočinac, L. D. R. (2011). Statistical convergence in function spaces, Abstr. Appl. Anal., Art. ID 420419, 11 pp. DOI: 10.1155/2011/420419
- [12] Megaritis, A. C. (2017). Ideal convergence of nets of functions with values in uniform spaces, Filomat 31(20), 6281– 6292. DOI: 10.2298/FIL1720281M
- [13] Osmanoğlu, İ. (2025). Statistical and Uniformly Statistical Convergence of Sequences of Functions, Filomat 39(30), Article in Press.
- [14] Georgiou, D. N., Megaritis, A. C., Özçağ, S. (2018). Statistical convergence of sequences of functions with values in semi-uniform spaces, Comment. Math. Univ. Carolin. 59(1), 103–117. DOI: 10.14712/1213-7243.2015.231
- [15] Maio, G. Di, Kočinac, L. D. R. (2008). Statistical convergence in topology, Topology Appl. 156, 28–45. DOI: 10.1016/j.topol.2008.01.015
- [16] Williams, J. (1972). Locally uniform spaces, Trans. Amer. Math. Soc. 168, 435–469. DOI: 10.1090/S0002-9947-1972-0296891-5
Öz
Bu çalışmada, yarı düzgün yakınsaklık topolojileri ile donatılmış fonksiyon uzaylarında istatistiksel yakınsaklığı incelemeye odaklanıyoruz. Bu topolojik yapılar altında noktasal ve düzgün istatistiksel yakınsamanın karşılaştırmalı bir analizini sağlıyor ve bu yakınsama türleri arasında geçişlere izin veren koşulları araştırıyoruz.
Anahtar Kelimeler
İstatistiksel yakınsama Yarı düzgün yakınsaklık topolojisi fonksiyon uzayları
Kaynakça
- [1] Kelley, J. L. (1975). General Topology, Springer, New York–Berlin.
- [2] Bourbaki, N. (1989). General Topology, Springer, Berlin.
- [3] Husek, M. (1964). Generalized proximity and uniform spaces I, Comment. Math. Univ. Carolinae, 5, 247–266.
- [4] Husek, M. (1965). Generalized proximity and uniform spaces II, Comment. Math. Univ. Carolinae, 6, 119–139.
- [5] Čech, E. (1966). Topological Spaces (revised by Z. Frolík and M. Katětov), Academia Publishing House of the Czechoslovak Academy of Sciences, Prague.
- [6] Page, W. (1989). Topological Uniform Structures, Dover Publications Inc., New York.
- [7] Fast, H. (1951). Sur la convergence statistique, Colloq. Math. 2, 241–244.
- [8] Steinhaus, H. (1951). Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2, 73–74.
- [9] Zygmund, A. (1979). Trigonometric Series (2nd ed.), Cambridge University Press, Cambridge.
- [10] Balcerzak, M., Dems, K., Komisarski, A. (2007). Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl. 328(1), 715–729. DOI: 10.1016/j.jmaa.2006.05.040
- [11] Caserta, A., Maio, G. Di., Kočinac, L. D. R. (2011). Statistical convergence in function spaces, Abstr. Appl. Anal., Art. ID 420419, 11 pp. DOI: 10.1155/2011/420419
- [12] Megaritis, A. C. (2017). Ideal convergence of nets of functions with values in uniform spaces, Filomat 31(20), 6281– 6292. DOI: 10.2298/FIL1720281M
- [13] Osmanoğlu, İ. (2025). Statistical and Uniformly Statistical Convergence of Sequences of Functions, Filomat 39(30), Article in Press.
- [14] Georgiou, D. N., Megaritis, A. C., Özçağ, S. (2018). Statistical convergence of sequences of functions with values in semi-uniform spaces, Comment. Math. Univ. Carolin. 59(1), 103–117. DOI: 10.14712/1213-7243.2015.231
- [15] Maio, G. Di, Kočinac, L. D. R. (2008). Statistical convergence in topology, Topology Appl. 156, 28–45. DOI: 10.1016/j.topol.2008.01.015
- [16] Williams, J. (1972). Locally uniform spaces, Trans. Amer. Math. Soc. 168, 435–469. DOI: 10.1090/S0002-9947-1972-0296891-5
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Deneysel Analiz |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 19 Kasım 2025 |
| Gönderilme Tarihi | 24 Nisan 2025 |
| Kabul Tarihi | 27 Ekim 2025 |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 9 Sayı: 2 |