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A generalized statistical convergence via ideals. (English) Zbl 1220.40004

The notion of \(\lambda\)-statistical convergence was introduced by Mursaleen [Math. Slovaca 50, No. 1, 111–115 (2000; Zbl 0953.40002)] as an extension of the \([V, \lambda]\) summability of L. Leindler [Publ. Math. 10, 274–282 (1964; Zbl 0129.05002)]. The authors introduce the concepts of \(I\)-\([V, \lambda]\)-summability and \(I\)-\(\lambda\)-statistical convergence by using ideals. They study the relation between these newly defined methods as well as the relation between \(I\)-\(\lambda\)-statistical convergence and \(I\)-statistical convergence.

MSC:

40A35 Ideal and statistical convergence
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[1] Fast, H., Sur la convergence ststistique, Colloq. Math., 2, 241-244 (1951) · Zbl 0044.33605
[2] Schoenberg, I. J., The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66, 361-375 (1959) · Zbl 0089.04002
[3] Fridy, J. A., On statistical convergence, Analysis, 5, 301-313 (1985) · Zbl 0588.40001
[4] Salat, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30, 139-150 (1980) · Zbl 0437.40003
[5] Kostyrko, P.; Salat, T.; Wilczynski, W., \(I\)-convergence, Real Anal. Exchange, 26, 2, 669-686 (2000/2001)
[6] Lahiri, B. K.; Das, Pratulananada, \(I\) and \(I^\ast \)-convergence in topological spaces, Math. Bohem., 130, 153-160 (2005) · Zbl 1111.40001
[7] Das, Pratulananda; Kostyrko, P.; Wilczynski, W.; Malik, P., \(I\) and \(I^\ast \)-convergence of double sequences, Math. Slovaca, 58, 5, 605-620 (2008) · Zbl 1199.40026
[8] Mursaleen, M., \( \lambda \)-statistical convergence, Math. Slovaca, 50, 111-115 (2000) · Zbl 0953.40002
[9] Leindler, L., Über die de la Vallée-Pousnsche Summierbarkeit allge meiner orthogonalreihen, Acta Math. Acad. Sci. Hungarica, 16, 375-387 (1965) · Zbl 0138.28802
[10] Kolk, E., The statistical convergence in Banach spaces, Acta Comment. Univ. Tartu, 928, 41-52 (1991)
[11] Pratulananda Das, Ekrem Savas, S. Ghosal, A new approach to certain summability methods using ideal, communicated.; Pratulananda Das, Ekrem Savas, S. Ghosal, A new approach to certain summability methods using ideal, communicated. · Zbl 1223.40004
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