A bounded consistency theorem for strong summabilities.
A challenging test for convergence accelerators: summation of a series with a special sign pattern.
A Characteriaztion of Conjugate WCG Banach Spaces.
A characterization of the Banach property for summability matrices
A class of conservative four-dimensional matrices.
A class of infinite series including terms of generalized sequences.
A class of statistical and -conservative matrices
In [5] and [10], statistical-conservative and -conservative matrices were characterized. In this note we have determined a class of statistical and -conservative matrices studying some inequalities which are analogous to Knopp’s Core Theorem.
A Classical Olivier’s Theorem and Statistical Convergence
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
A complex Tauberian theorem and mean ergodic semigroups.
A complex-variable proof of the Wiener tauberian theorem
The fundamental semigroup of the heat equation for the real line has an analytic extension to the right-hand open half plane which satisfies for Re. Using the Ahlfors-Heins theorem for bounded analytic functions on a half-plane we show that the Wiener tauberian theorem for follows from the above inequality.
A continued fraction expansion for a -tangent function: an elementary proof.
A convergence theory of some methods of integration.
A convolution relation with remainder estimate.
A formula for calculation of metric dimension of converging sequences
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
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.
A general note on increasing sequences.
A general theorem covering many absolute summability methods
A general theorem concerning many absolute summability methods is proved.
A general theorem on Nörlund summability of Fourier series with applications