MATHEMATICA BOHEMICA, Vol. 130, No. 2, pp. 177-184 (2005)

Remarks on statistical and $I$-convergence of series

J. Cervenansky, T. Salat, V. Toma

J. Cervenansky, Faculty of Materials Science and Technology, Slovak University of Technology, Paulinska 16, 917 24 Trnava; T. Salat, V. Toma, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska dolina, 842 48 Bratislava, e-mail: toma@fmph.uniba.sk

Abstract: In this paper we investigate the relationship between the statistical (or generally $I$-convergence) of a series and the usual convergence of its subseries. We also give a counterexample which shows that Theorem 1 of the paper by B. C. Tripathy "On statistically convergent series", Punjab. Univ. J. Math. 32 (1999), 1-8, is not correct.

Keywords: statistical convergence, $I$-convergence, $I$-convergent series

Classification (MSC2000): 40A05, 54A20

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