Research Article
Year 2025,
Volume: 9 Issue: 2, 78 - 83
Abstract
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.
References
- [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
Year 2025,
Volume: 9 Issue: 2, 78 - 83
Abstract
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.
References
- [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
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Experimental Mathematics |
| Journal Section | Research Article |
| Authors | |
| Publication Date | November 18, 2025 |
| Submission Date | April 24, 2025 |
| Acceptance Date | October 27, 2025 |
| Published in Issue | Year 2025 Volume: 9 Issue: 2 |
Aksaray J. Sci. Eng. | e-ISSN: 2587-1277 | Period: Biannually | Founded: 2017 | Publisher: Aksaray University | https://asujse.aksaray.edu.tr
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