Savas, Ekrem; Das, Pratulananda A generalized statistical convergence via ideals. (English) Zbl 1220.40004 Appl. Math. Lett. 24, No. 6, 826-830 (2011). 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. Reviewer: İbrahim Çanak (İzmir) Cited in 7 ReviewsCited in 84 Documents MSC: 40A35 Ideal and statistical convergence Keywords:ideal; filter; \(I\)-statistical convergence; \(I\)-\(\lambda\)-statistical convergence; \(I\)-\([V, \lambda]\)-summability; closed subspace Citations:Zbl 0953.40002; Zbl 0129.05002 PDFBibTeX XMLCite \textit{E. Savas} and \textit{P. Das}, Appl. Math. Lett. 24, No. 6, 826--830 (2011; Zbl 1220.40004) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.