Weighted Statistical Limit Supremum-Infimum

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

1. Adem A. A., Altınok M.,Weighted Statistical Convergence of Real Valued Sequences, Facta Universitatis, Series: Mathematics and Informatics, 35(3)(2020), 887–898.
2. Altınok M., Küçükaslan M., Statistical supremum-infimum and statistical convergence, The Aligarh Bulletin of Mathematics, 32(2013), 1–16.
3. Altınok M., Küçükaslan M., A-statistical supremum-infimum and A-statistical convergence, Azerbaijan Journal of Mathematics, 4(2)(2014), 31–42.
4. Balcerzak M., Das P., Filipczak M., Swaczyna J., Generalized kinds of density and the associated ideals, Acta Math. Hungar., 147(1)(2015), 97–115.
5. Bhunia S., Das P., Pal S. K., Restricting statistical convergence, Acta Mathematica Hungarica, 134(1-2)(2012), 153–161.
6. Buck, C., Generalized asymptotic density, Amer. J. Math., 75(1953), 335-346.
7. Cakalli, H., A new approach to statistically quasi Cauchy sequences, Maltepe Journal of Mathematics, 1(1)(2019), 1-8.
8. Connor J., The statistical and strong p-Cesaro convergence of sequences, Analysis, 8(1988), 47–63.

9. Connor J., On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32(1989), 194–198.
10. Çolak R., Statistical convergence of order $\alpha$, Modern Methods in Analysis and Its Applications, Anamaya Pub., New Delhi, India, 2010.
11. 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.
12. Fast H., Sur la convergence statistique, Colloq. Math., 2(1951), 241–244.
13. Freedman A. P., Sember J. J., Densities and summability, Pasific J. Math., 95(1981), 293–305.
14. Fridy J. A., On statistical convergence, Analysis, 5(1985), 1301–1313.
15. Fridy J. A., Statistical limit points, Proc. Amer. Math. Soc., 118(1993), 1187–1192.
16. Hardy G. H., Divergent Series, Oxford Univ. Press, London 1949.
17. Sengul Kandemir, H., On I-Deferred statistical convergence in topological groups}, Maltepe Journal of Mathematics, 1(2)(2019), 48-55.
18. Knopp K., Zur Theorie der Limitierungsverfahren (Erste Mitteilung), Math. Zeit., 31(1930), 115–127.
19. Kostyrko P, Macaj M., Salat T., Strauch O., On statistical limit points, Proc. Amer. Math. Soc., 120(2000), 2647–2654.
20. Schoenberg, I.J., The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(5)(1959), 361-375.
21. Steinhaus, H., Sur la convergence ordinate et la convergence asymptotique, Colloq. Math., 2(1951), 73-84.
22. Taylan, I., Abel statistical delta quasi Cauchy sequences of real numbers, Maltepe Journal of Mathematics, 1(1)(2019), 18-23.
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.
24. Zygmund, A., Trigonometric Series, Cambridge Univ. Press, Cambridge, UK, 1979.