Öz
Kaynakça
- Alt\i nok. M, K\"u\c{c}\"ukaslan. M, A-Statistical Supremum-Infimum and A-Statistical Convergence, Azerbaijan Journal of Mathematics, Vol.4, No.2, pp.43-57, (2014).
- Alt\i nok. M, K\"u\c{c}\"ukaslan. M, Ideal Limit Superior-Inferior, Gazi University Journal of Science, Vol.30, No.1, pp.401-411, (2017).
- Alt\i nok. M, Porosity Supremum-Infimum and Porosity Convergence, Konuralp Journal of Mathematics, Vol.6, No.1, pp.163-170, (2018).
- Fast. H, Sur la convergence statistique., Colloq. Math, Vol.2, pp.241-244, (1951).
- Fridy. J. A, On statistical convergence, Analysis, Vol.5, pp.301-313, (1985).
- K\"u\c{c}\"ukaslan. M, Alt\i nok. M, Statistical supremum infimum and statistical convergence, Aligarh Bulletin of Mathematics, Vol.32, pp.1-16, (2013).
- Milan. P, Density and related topics, Mathematics Institute Slovak Academic of Sciences (2017).
- Schoenberg. I. J, The integrability of certain functions and related summability methods, matrix characterization of statistical convergence, Amer.Math., Vol.66, pp.361-375, (1959).
- Steinhaus. H, Sur la convergence ordinaire at la convergence asymptotique, Colloq. Math., Vol.2, No.1, pp.73-74, (1951).
- Zygmund. A, Trigonometric series, 2nd., Ed. Vol. II, Cambridge Univ. press, London and New York (1979).
Öz
Convergence of real valued sequences especially statistical convergence is very popular subject in Mathematical Analysis. Also, it has got a lot of characterizations in literature. In this paper, we are going to define $\lambda$-statistical supremum and $\lambda$-statistical infimum for real valued sequence $x=(x_n)$. After giving some basic properties of these new notations, then we are going to find a necessary and sufficient condition for to existence of λ-statistical convergence of the sequence $x=(x_n)$.
Anahtar Kelimeler
Statistical supremum-infimum Statistical convergence Natural density
Kaynakça
- Alt\i nok. M, K\"u\c{c}\"ukaslan. M, A-Statistical Supremum-Infimum and A-Statistical Convergence, Azerbaijan Journal of Mathematics, Vol.4, No.2, pp.43-57, (2014).
- Alt\i nok. M, K\"u\c{c}\"ukaslan. M, Ideal Limit Superior-Inferior, Gazi University Journal of Science, Vol.30, No.1, pp.401-411, (2017).
- Alt\i nok. M, Porosity Supremum-Infimum and Porosity Convergence, Konuralp Journal of Mathematics, Vol.6, No.1, pp.163-170, (2018).
- Fast. H, Sur la convergence statistique., Colloq. Math, Vol.2, pp.241-244, (1951).
- Fridy. J. A, On statistical convergence, Analysis, Vol.5, pp.301-313, (1985).
- K\"u\c{c}\"ukaslan. M, Alt\i nok. M, Statistical supremum infimum and statistical convergence, Aligarh Bulletin of Mathematics, Vol.32, pp.1-16, (2013).
- Milan. P, Density and related topics, Mathematics Institute Slovak Academic of Sciences (2017).
- Schoenberg. I. J, The integrability of certain functions and related summability methods, matrix characterization of statistical convergence, Amer.Math., Vol.66, pp.361-375, (1959).
- Steinhaus. H, Sur la convergence ordinaire at la convergence asymptotique, Colloq. Math., Vol.2, No.1, pp.73-74, (1951).
- Zygmund. A, Trigonometric series, 2nd., Ed. Vol. II, Cambridge Univ. press, London and New York (1979).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Gönderilme Tarihi | 8 Kasım 2020 |
| Kabul Tarihi | 18 Şubat 2021 |
| Yayımlanma Tarihi | 31 Ocak 2021 |
| DOI | https://doi.org/10.33773/jum.823084 |
| IZ | https://izlik.org/JA83SF38AH |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 4 Sayı: 1 |