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Some new facts about group 𝒢 generated by the family of convergent permutations

Roman Wituła, Edyta Hetmaniok, Damian Słota (2017)

Open Mathematics

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 remarks on I -faster convergent infinite series

Ladislav Matejíčka (2009)

Mathematica Bohemica

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 defined by Orlicz functions

Ekrem Savaş, Rahmet Savaş (2004)

Archivum Mathematicum

In this paper we introduce a new concept of λ -strong convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces. It is also shown that if a sequence is λ -strongly convergent with respect to an Orlicz function then it is λ -statistically convergent.

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