Weighted Statistical Limit Supremum-Infimum

Year 2022, Volume: 14 Issue: 1, 16 - 23, 30.06.2022

Maya Altınok

https://doi.org/10.47000/tjmcs.975585

https://izlik.org/JA96MK23JN

Abstract

In this paper, by using weight $g$-statistical density we introduce weight $g$-statistical supremum-infimum for real valued sequences. We also define weight $g$-statistical limit supremum-infimum with the help of above new concepts. In addition, we shall establish some results about weight $g$-statistical core.

Keywords

Weighted density , Weighted statistical limit supremum-infimum , weighted statistical core

References

• Adem A. A., Altınok M.,Weighted Statistical Convergence of Real Valued Sequences, Facta Universitatis, Series: Mathematics and Informatics, 35(3)(2020), 887–898.
• Altınok M., Küçükaslan M., Statistical supremum-infimum and statistical convergence, The Aligarh Bulletin of Mathematics, 32(2013), 1–16.
• Altınok M., Küçükaslan M., A-statistical supremum-infimum and A-statistical convergence, Azerbaijan Journal of Mathematics, 4(2)(2014), 31–42.
• Balcerzak M., Das P., Filipczak M., Swaczyna J., Generalized kinds of density and the associated ideals, Acta Math. Hungar., 147(1)(2015), 97–115.
• Bhunia S., Das P., Pal S. K., Restricting statistical convergence, Acta Mathematica Hungarica, 134(1-2)(2012), 153–161.
• Buck, C., Generalized asymptotic density, Amer. J. Math., 75(1953), 335-346.
• Cakalli, H., A new approach to statistically quasi Cauchy sequences, Maltepe Journal of Mathematics, 1(1)(2019), 1-8.
• Connor J., The statistical and strong p-Cesaro convergence of sequences, Analysis, 8(1988), 47–63.
• Connor J., On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32(1989), 194–198.
• Çolak R., Statistical convergence of order $\alpha$, Modern Methods in Analysis and Its Applications, Anamaya Pub., New Delhi, India, 2010.
• Das P., Savas¸ E., On generalized statistical and ideal convergence of metric-valued sequences, Reprinted in Ukrainian Math. J., 68(12)(2017), 1849–1859. Ukrain. Mat. Zh., 68(12)(2016), 1598–1606.
• Fast H., Sur la convergence statistique, Colloq. Math., 2(1951), 241–244.
• Freedman A. P., Sember J. J., Densities and summability, Pasific J. Math., 95(1981), 293–305.
• Fridy J. A., On statistical convergence, Analysis, 5(1985), 1301–1313.
• Fridy J. A., Statistical limit points, Proc. Amer. Math. Soc., 118(1993), 1187–1192.
• Hardy G. H., Divergent Series, Oxford Univ. Press, London 1949.
• Sengul Kandemir, H., On I-Deferred statistical convergence in topological groups}, Maltepe Journal of Mathematics, 1(2)(2019), 48-55.
• Knopp K., Zur Theorie der Limitierungsverfahren (Erste Mitteilung), Math. Zeit., 31(1930), 115–127.
• Kostyrko P, Macaj M., Salat T., Strauch O., On statistical limit points, Proc. Amer. Math. Soc., 120(2000), 2647–2654.
• Schoenberg, I.J., The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(5)(1959), 361-375.
• Steinhaus, H., Sur la convergence ordinate et la convergence asymptotique, Colloq. Math., 2(1951), 73-84.
• Taylan, I., Abel statistical delta quasi Cauchy sequences of real numbers, Maltepe Journal of Mathematics, 1(1)(2019), 18-23.
• Tok, N., Basarir, M., On the lambda alpha h statistical convergence of the functions defined on the time scale, Proceedings of International Mathematical Sciences, 1(1)(2019), 1-10.
• Zygmund, A., Trigonometric Series, Cambridge Univ. Press, Cambridge, UK, 1979.