Abstract
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 will discuss some questions related to the convergence of subseries of a given series.
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References
R. C. Buck and H. Pollard: Convergence and summability properties of subsequences. Bull. Amer. Math. Soc. 49 (1943), 924–931.
R. G. Cooke: Infinite Matrices and Sequence Spaces (Russian Edition). Moscow, 1960.
M. Dindoš, I. Martišovitš and T. Salát: Remarks on infinite series in linear normed spaces. Tatra Mt. Math. Publ. 19 (2000), 31–46.
R. Durret: Probability: Theory and Examples. Duxbury Press, 1995.
H. Fast: Sur la convergence statistique. Coll. Math. 2 (1951), 241–244.
J. A. Fridy: On statistical convergence. Analysis 5 (1985), 301–313.
P. Kostyrko, M. Ma£aj and T. Salát: Statistical convergence and I-convergence. To appear in Real Anal. Exch.
H. H. Ostmann: Additive Zahlentheorie I. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956.
T.Salát: On Hausdorff measure of linear sets. Czechoslovak Math. J. 11 (86) (1980), 24–56. (In Russian.)
T. Salát: On subseries. Math. Zeit. 85 (1964), 209–225.
T. Salát: Über die Cantorsche Reihen. Czechoslovak Math. J. 18 (93) (1968), 25–56.
T. Salát: On subseries of divergent series. Mat. Éas. SAV 18 (1968), 312–338.
T. Salát: On statistically convergent sequences of real numbers. Math. Slovaca 30 (1980), 139–150.
I. J. Schoenberg: The integrability of certain functions and related summability methods. Amer. Math. Monthly 66 (1959), 361–375.
C. Visser: The law of nought-or-one. Studia Math. 7 (1938), 143–159.
B. C. Tripathy: On statistically convergence series. Punjab University J. Math. XXXXII (1999), 1–8.
B. C. Tripathy: On statistical convergence. Proc. Estonian Acad. Sci. Phys. Math. 47 (1998), 299–303.
A. Zygmund: Trigonometric series I. MIR, Moscow, 1965. (In Russian.)
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Dindoš, M., Šalát, T. & Toma, V. Statistical Convergence of Infinite Series. Czech Math J 53, 989–1000 (2003). https://doi.org/10.1023/B:CMAJ.0000024535.89828.e8
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DOI: https://doi.org/10.1023/B:CMAJ.0000024535.89828.e8