Topic
Almost convergent sequence
About: Almost convergent sequence is a research topic. Over the lifetime, 18 publications have been published within this topic receiving 137 citations.
Papers
1 Mar 1979
TL;DR: The concept of strong almost convergence was introduced in this paper, where the matrices summing every strongly almost convergent sequence, leaving the limit invariant, were characterized, and the concept of strongly almost convergence is introduced.
Abstract: The concept of strong almost convergence was introduced in (2), where the matrices summing every strongly almost convergent sequence, leaving the limit invariant, were characterized.
71 citations
TL;DR: In this article, the Euler totient matrix has been used to study the almost convergent sequence space and it is proved that the space is linearly isomorphic with the space of all almost convergegent sequences.
Abstract: This paper is devoted to study the almost convergent sequence space
$$\widehat{c}(\varPhi )$$
derived by the Euler totient matrix. It is proved that the space
$$\widehat{c}(\varPhi )$$
and the space of all almost convergent sequences are linearly isomorphic. Further, the
$$\beta $$
-dual of the space
$$\widehat{c}(\varPhi )$$
is determined and Euler totient core of a complex-valued sequence has been defined. Finally, inclusion theorems related to this new type of core are obtained.
17 citations
TL;DR: In this article, the applications of fractional-order difference operators were studied by generating almost null and almost convergent sequence spaces, which are linearly isomorphic and BK-spaces.
Abstract: In the present paper, we intend to make an approach to introduce and study the applications of fractional-order difference operators by generating Orlicz almost null and almost convergent sequence spaces. We also show that aforesaid spaces are linearly isomorphic and BK-spaces. Further, we investigate inclusion relations between newly formed sequence spaces and compute the β -, γ -duals. Moreover, we characterize several classes of infinite matrices and give some interesting examples. Finally, we study aforesaid sequence spaces over n-normed space and demonstrate their several algebraic and topological properties.
9 citations
TL;DR: In this article, the authors introduce the notions of upper weight, lower weight and weight of subsequences of natural numbers and investigate some new estimations about Banach limits by using some results from Sucheston.
8 citations
1 Jan 2015
TL;DR: In this paper, the authors introduce the spacesfs(4 (m) ), f(4 m) and f0(m) that consist of all sequence whose 4 m transforms are in the set of almost convergent sequence and series spaces.
Abstract: This paper is mainly concerned with introducing the spacesfs(4 (m) ), f(4 (m) ) and f0(4 (m) ) that consist of all sequence whose4 (m) transforms are in the set of almost convergent sequence and series spaces. Certain topological properties of these new almost convergent sets have been investigated as well as and duals of the spaces fs(4 (m) ) and f(4 (m) ). In addition to that the non-existence of Schauder basis of the spaces fs and fs( (m) ) is shown. Furthermore, the characterization of certain matrix classes on/into the sets of generalized dierence almost convergent sequence and series has exhaustively
8 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 2 |
| 2016 | 1 |
| 2015 | 2 |
| 2013 | 1 |
| 2012 | 2 |