Abstract
Bu makalede, tam sayı ikilileri için verilen yoğunluk kavramının bir
genelleştirilmesi olan αβ doğal yoğunluk kavramını
tanımladık. Bu yoğunluk kavramı yardımıyla çift diziler için αβ-istatistiksel E-yakınsaklık kavramı tanıtıldı. Daha sonra
bu tip yakınsaklığın temel özellikleri incelendi. Ayrıca, E-anlamında
αβ-istatistiksel alt limit ve üst limit
kavramlarını tanımladık. Son olarak bu kavramlarla ilgili teoremler verdik.
Keywords
Çift dizi E-yakınsaklık İstatistiksel Yakınsaklık αβ-istatistiksel E-yakınsaklık αβ-istatistiksel E-alt limit ve üst limit
References
- Aktuğlu, H. 2014. Korovkin type approximation theorems proved via αβ-statistical convergence. Journal of Computational and Applied Mathematics, 259, 174--181.
- Boos, J., Leiger, T. and Zeller, K. 1997. Consistency theory for SM-methods. Acta Mathematica Hungarica, 76, 83--116.
- Çakan, C. and Altay, B. 2006. Statistically boundedness and statistical core of double sequences. Journal of Mathematical Analysis and Applications, 317, 690--697.
- Edely, O. H. H. and Mursaleen, M. 2006. Tauberian theorems for statistically convergent double sequences. Information Sciences, 176, 875--886.
- Fast, H. 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241--244.
- Fridy, J. A. and Orhan, C. 1997. Statistical limit superior and limit inferior. Proceedings of the American Mathematical Society, 125(12), 3625--3631.
- Hardy, G. H. 1917. On the convergence of certain multiple series. Mathematical Proceedings of the Cambridge Philosophical Society, 19, 86--95.
- Karaisa A. 2016. Statistical αβ-Summability and Korovkin Type Approximation Theorem. Filomat, 30(13), 3483--3491.
- Móricz, F. 2003. Statistical convergence of multiple sequences. Archiv der Mathematik (Basel), 81(1), 82--89.
- Mursaleen, M. and Edely, O. H. H. 2003. Statistical convergence of double sequences. Journal of Mathematical Analysis and Applications, 288, 223--231.
- Pringsheim, A. 1898. Elementare theorie der unendliche doppelreihen. Sitsungs berichte der Math. Akad. der Wissenschafftenzu Münch. Ber., 7, 101--153.
- Sever, Y. and Talo, Ö. 2014. e-core of double sequences. Acta Mathematica Hungarica, 144(1), 236--246.
- Sever, Y. and Talo, Ö. 2017. Statistical e-convergence of double sequences and its application to Korovkin type approximation theorem for functions of two variables. Iranian Journal of Science and Technology. Transaction A. Science, 41(3), 851--857.
- Sever, Y. and Talo, Ö. 2018. On statistical e-convergence of double sequences. Iranian Journal of Science and Technology. Transaction A. Science, 42(4), 2063--2068.
- Zeltser, M. 2001. Investigation of double sequence spaces by soft and hard analitical methods. Dissertationes Mathematicae Universitatis Tartuensis 25, Tartu University Press, Univ. of Tartu, Faculty of Mathematics and Computer Science, (Tartu).
- Zeltser, M. 2002. On conservative matrix methods for double sequence spaces. Acta Mathematica Hungarica, 95(3), 225--242.
Abstract
References
- Aktuğlu, H. 2014. Korovkin type approximation theorems proved via αβ-statistical convergence. Journal of Computational and Applied Mathematics, 259, 174--181.
- Boos, J., Leiger, T. and Zeller, K. 1997. Consistency theory for SM-methods. Acta Mathematica Hungarica, 76, 83--116.
- Çakan, C. and Altay, B. 2006. Statistically boundedness and statistical core of double sequences. Journal of Mathematical Analysis and Applications, 317, 690--697.
- Edely, O. H. H. and Mursaleen, M. 2006. Tauberian theorems for statistically convergent double sequences. Information Sciences, 176, 875--886.
- Fast, H. 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241--244.
- Fridy, J. A. and Orhan, C. 1997. Statistical limit superior and limit inferior. Proceedings of the American Mathematical Society, 125(12), 3625--3631.
- Hardy, G. H. 1917. On the convergence of certain multiple series. Mathematical Proceedings of the Cambridge Philosophical Society, 19, 86--95.
- Karaisa A. 2016. Statistical αβ-Summability and Korovkin Type Approximation Theorem. Filomat, 30(13), 3483--3491.
- Móricz, F. 2003. Statistical convergence of multiple sequences. Archiv der Mathematik (Basel), 81(1), 82--89.
- Mursaleen, M. and Edely, O. H. H. 2003. Statistical convergence of double sequences. Journal of Mathematical Analysis and Applications, 288, 223--231.
- Pringsheim, A. 1898. Elementare theorie der unendliche doppelreihen. Sitsungs berichte der Math. Akad. der Wissenschafftenzu Münch. Ber., 7, 101--153.
- Sever, Y. and Talo, Ö. 2014. e-core of double sequences. Acta Mathematica Hungarica, 144(1), 236--246.
- Sever, Y. and Talo, Ö. 2017. Statistical e-convergence of double sequences and its application to Korovkin type approximation theorem for functions of two variables. Iranian Journal of Science and Technology. Transaction A. Science, 41(3), 851--857.
- Sever, Y. and Talo, Ö. 2018. On statistical e-convergence of double sequences. Iranian Journal of Science and Technology. Transaction A. Science, 42(4), 2063--2068.
- Zeltser, M. 2001. Investigation of double sequence spaces by soft and hard analitical methods. Dissertationes Mathematicae Universitatis Tartuensis 25, Tartu University Press, Univ. of Tartu, Faculty of Mathematics and Computer Science, (Tartu).
- Zeltser, M. 2002. On conservative matrix methods for double sequence spaces. Acta Mathematica Hungarica, 95(3), 225--242.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | March 17, 2020 |
| Submission Date | October 26, 2019 |
| Published in Issue | Year 2020 Volume: 20 Issue: 1 |
Cite
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.