×

Statistical convergence of infinite series. (English) Zbl 1080.40500

Summary: In this paper we use the notion of statistical convergence of infinite series naturally introduced as the statistical convergence of the sequence of the partial sums of the series. We discuss some questions related to the convergence of subseries of a given series.

MSC:

40A05 Convergence and divergence of series and sequences
PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[1] R. C. Buck and H. Pollard: Convergence and summability properties of subsequences. Bull. Amer. Math. Soc. 49 (1943), 924-931. · Zbl 0060.15803
[2] R. G. Cooke: Infinite Matrices and Sequence Spaces (Russian Edition). Moscow, 1960.
[3] M. Dindoš, I. Martišovitš and T. Šalát: Remarks on infinite series in linear normed spaces. Tatra Mt. Math. Publ. 19 (2000), 31-46. · Zbl 0984.40001
[4] R. Durret: Probability: Theory and Examples. Duxbury Press, 1995.
[5] H. Fast: Sur la convergence statistique. Coll. Math. 2 (1951), 241-244. · Zbl 0044.33605
[6] J. A. Fridy: On statistical convergence. Analysis 5 (1985), 301-313. · Zbl 0588.40001
[7] P. Kostyrko, M. Mačaj and T. Šalát: Statistical convergence and I-convergence. To appear in Real Anal. Exch.
[8] H. H. Ostmann: Additive Zahlentheorie I. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956. · Zbl 0072.03101
[9] T. Šalát: On Hausdorff measure of linear sets. Czechoslovak Math. J. 11 (86) (1980), 24-56.
[10] T. Šalát: On subseries. Math. Zeit. 85 (1964), 209-225. · Zbl 0127.28801
[11] T. Šalát: Über die Cantorsche Reihen. Czechoslovak Math. J. 18 (93) (1968), 25-56. · Zbl 0157.09904
[12] T. Šalát: On subseries of divergent series. Mat. Čas. SAV 18 (1968), 312-338. · Zbl 0169.07201
[13] T. Šalát: On statistically convergent sequences of real numbers. Math. Slovaca 30 (1980), 139-150. · Zbl 0437.40003
[14] I. J. Schoenberg: The integrability of certain functions and related summability methods. Amer. Math. Monthly 66 (1959), 361-375. · Zbl 0089.04002
[15] C. Visser: The law of nought-or-one. Studia Math. 7 (1938), 143-159. · Zbl 0019.22501
[16] B. C. Tripathy: On statistically convergence series. Punjab University J. Math. XXXXII (1999), 1-8. · Zbl 0966.40003
[17] B. C. Tripathy: On statistical convergence. Proc. Estonian Acad. Sci. Phys. Math. 47 (1998), 299-303. · Zbl 0961.40002
[18] A. Zygmund: Trigonometric series I. MIR, Moscow, 1965. · Zbl 0131.06703
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.