Series like Taylor's series.
Series of iterates
Set-theoretic characteristics of summability of sequences and convergence of series
Silvermann-Toeplitz theorem for double sequences and series and its application to Nörlund means in non-archimedean fields
Some Characterizations Of Almost Convergence For Single And Double Sequences
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 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 regularity properties of algorithms and additive functions with respect to them.
Some remarks on -faster convergent infinite series
A structure of terms of -faster convergent series is studied in the paper. Necessary and sufficient conditions for the existence of -faster convergent series with different types of their terms are proved. Some consequences are discussed.
Some results on convergence acceleration for the E-algorithm
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.
Some sequence spaces defined by a modulus