Some applications of Tauberian theorems in probability theory.
Some Characterizations Of Almost Convergence For Single And Double Sequences
Some footprints of Marcinkiewicz in summability theory
Four basic results of Marcinkiewicz are presented in summability theory. We show that setting out from these theorems many mathematicians have reached several nice results for trigonometric, Walsh- and Ciesielski-Fourier series.
Some generalisations on a scale of Abel type summability methods
Some generalizations of Olivier's theorem
Let be a convergent series of positive real numbers. L. Olivier proved that if the sequence is non-increasing, then . In the present paper: (a) We formulate and prove a necessary and sufficient condition for having ; Olivier’s theorem is a consequence of our Theorem . (b) We prove properties analogous to Olivier’s property when the usual convergence is replaced by the -convergence, that is a convergence according to an ideal of subsets of . Again, Olivier’s theorem is a consequence of...
Some inclusion theorems for absolute summability
Some integrability theorems for multiple trigonometric series
Several new integrability theorems are proved for multiple cosine or sine series.
Some Mazur-Orlicz-Brudno like theorems
Some Mercerian Theorems For Regularly Varying Sequences
Some more Steinhaus type theorems over valued fields
Some new bounds for Mathieu's series.
Some new facts about group 𝒢 generated by the family of convergent permutations
The aim of this paper is to present some new and essential facts about group 𝒢 generated by the family of convergent permutations, i.e. the permutations on ℕ preserving the convergence of series of real terms. We prove that there exist permutations preserving the sum of series which do not belong to 𝒢. Additionally, we show that there exists a family G (possessing the cardinality equal to continuum) of groups of permutations on ℕ such that each one of these groups is different than 𝒢 and is composed...
Some new Properties of Sequence Spaces and Application to the Continued Fractions
Some new sequence spaces defined by a modulus function
Some new sequence spaces defined by lacunary sequences
Some Observations on the Distribution of Values of Continued Fractions.
Some problems and solutions involving Mathieu's series and its generalizations.
Some properties of a function connected to a double series.
Some properties of Banach-valued sequence spaces .
Some properties of Riesz means and spectral expansions. (With an appendix by R. A. Gustafson).