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A structure of terms of $I$ -faster convergent series is studied in the paper. Necessary and sufficient conditions for the existence of $I$ -faster convergent series with different types of their terms are proved. Some consequences are discussed.

Some results on convergence acceleration for the E-algorithm

A. Fdil (1997)

Applicationes Mathematicae

Some new results on convergence acceleration for the E-algorithm which is a general extrapolation method are obtained. A technique for avoiding numerical instability is proposed. Some applications are given. Theoretical results are illustrated by numerical experiments

Some sequence spaces and statistical convergence.

Savaş, E. (2002)

International Journal of Mathematics and Mathematical Sciences

Some sequence spaces defined by a modulus

Serpil Pehlivan, Brian Fisher (1995)

Mathematica Slovaca

Some statistically convergent difference sequence spaces defined over real 2-normed linear spaces.

Dutta, Hemen (2010)

APPS. Applied Sciences

Sommation de certains développements

Désiré André (1871)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Spherical summation : a problem of E.M. Stein

Antonio Cordoba, B. Lopez-Melero (1981)

Annales de l'institut Fourier

Writing $(T_{R}^{λ} f) \hat{} (ξ) = (1 - | ξ |^{2} / R^{2})_{+}^{λ} \hat{f} (ξ)$ . E. Stein conjectured $∥ {(\sum_{j} | T_{R_{j}}^{λ} f_{i} |^{2})}^{1 / 2} ∥_{p} \leq C ∥ {(\sum_{j} | f_{j} |^{2})}^{1 / 2} ∥_{p}$ for $λ > 0$ , $\frac{4}{3} \leq p \leq 4$ and $C = C_{λ, p}$ . We prove this conjecture. We prove also $f (x) = {lim}_{j \to \infty} T_{2^{j}}^{λ} f (x)$ a.e. We only assume $\frac{4}{3 + 2 λ} < p < \frac{4}{1 - 2 λ}$ .

Stacked exponents.

J.J. Andrews, R.C. Lacher (1977)

Aequationes mathematicae

Stacked exponents. (Short Communication).

J.J. Andrews, R.C. Lacher (1977)

Aequationes mathematicae

Stanovení součtů jistých nekonečných řad

Eduard Weyr (1892)

Časopis pro pěstování mathematiky a fysiky

Statistical cluster points of sequences in finite dimensional spaces

Serpil Pehlivan, A. Güncan, M. A. Mamedov (2004)

Czechoslovak Mathematical Journal

In this paper we study the set of statistical cluster points of sequences in $m$ -dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in $m$ -dimensional spaces too. We also define a notion of $Γ$ -statistical convergence. A sequence $x$ is $Γ$ -statistically convergent to a set $C$ if $C$ is a minimal closed set such that for every $ϵ > 0$ the set ${k ρ (C, x_{k}) \geq ϵ}$ has density zero. It is shown that every statistically bounded sequence...

Statistical convergence of a sequence of random variables and limit theorems

Sanjoy Ghosal (2013)

Applications of Mathematics

In this paper the ideas of three types of statistical convergence of a sequence of random variables, namely, statistical convergence in probability, statistical convergence in mean of order $r$ and statistical convergence in distribution are introduced and the interrelation among them is investigated. Also their certain basic properties are studied.

Statistical convergence of double sequences on probabilistic normed spaces.

Karakus, S., Demırcı, K. (2007)

International Journal of Mathematics and Mathematical Sciences

Statistical convergence of infinite series

M. Dindoš, Tibor Šalát, Vladimír Toma (2003)

Czechoslovak Mathematical Journal

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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