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In [5] and [10], statistical-conservative and $σ$ -conservative matrices were characterized. In this note we have determined a class of statistical and $σ$ -conservative matrices studying some inequalities which are analogous to Knopp’s Core Theorem.

A Classical Olivier’s Theorem and Statistical Convergence

Tibor Šalát, Vladimír Toma (2003)

Annales mathématiques Blaise Pascal

L. Olivier proved in 1827 the classical result about the speed of convergence to zero of the terms of a convergent series with positive and decreasing terms. We prove that this result remains true if we omit the monotonicity of the terms of the series when the limit operation is replaced by the statistical limit, or some generalizations of this concept.

A comparison theorem for weighted mean and Cesàro methods

Billy E. Rhoades (1996)

Mathematica Slovaca

A complex Tauberian theorem and mean ergodic semigroups.

W. Arendt, C.J.K. Batty (1995)

Semigroup forum

A complex-variable proof of the Wiener tauberian theorem

Jean Esterlé (1980)

Annales de l'institut Fourier

The fundamental semigroup $(a^{t})_{t > 0}$ of the heat equation for the real line has an analytic extension $(a^{t})_{Re t > 0}$ to the right-hand open half plane which satisfies $∥ a^{t} ∥ \leq \sqrt{| t |}$ for Re $t \geq 1$ . Using the Ahlfors-Heins theorem for bounded analytic functions on a half-plane we show that the Wiener tauberian theorem for $L^{1} (R)$ follows from the above inequality.

A continued fraction expansion for a $q$ -tangent function: an elementary proof.

Prodinger, Helmut (2008)

Séminaire Lotharingien de Combinatoire [electronic only]

A convergence theory of some methods of integration.

P. Wynn (1976)

Journal für die reine und angewandte Mathematik

A convolution relation with remainder estimate.

G.S. Jordan (1976)

Journal für die reine und angewandte Mathematik

A formula for calculation of metric dimension of converging sequences

Ladislav, Jr. Mišík, Tibor Žáčik (1999)

Commentationes Mathematicae Universitatis Carolinae

Converging sequences in metric space have Hausdorff dimension zero, but their metric dimension (limit capacity, entropy dimension, box-counting dimension, Hausdorff dimension, Kolmogorov dimension, Minkowski dimension, Bouligand dimension, respectively) can be positive. Dimensions of such sequences are calculated using a different approach for each type. In this paper, a rather simple formula for (lower, upper) metric dimension of any sequence given by a differentiable convex function, is derived....

A function related to a Lagrange-Bürmann series

Paul Bracken (2002)

Czechoslovak Mathematical Journal

An infinite series which arises in certain applications of the Lagrange-Bürmann formula to exponential functions is investigated. Several very exact estimates for the Laplace transform and higher moments of this function are developed.

A General Extrapolation Algorithm.

C. Brezinski (1980)

Numerische Mathematik

A general note on increasing sequences.

Bor, Hüseyin (2007)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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