On domain of Nörlund matrix
type: Item
instance of: scholarly article
title: On domain of Nörlund matrix
zbMATH Open document ID: 1411.40005
author: Kuddusi Kayaduman
author: Fevzi Yaşar
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: Summary: In 1978, the domain of the Nörlund matrix on the classical sequence spaces \(l_p\) and \(l_\infty\) was introduced by \textit{C.-S Wang}, Tamkang J. Math. 9, 269--274 (1979; Zbl 0415.46009), where \(1\leq p<\infty\). \textit{O. Tuğ} and \textit{F. Başar} studied the matrix domain of Nörlund mean on the sequence spaces \(f_0\) and \(f\) in [Filomat 30, No.~3, 773--783 (2016; Zbl 1462.46009)]. Additionally, \textit{O. Tuğ} defined and investigated a new sequence space as the domain of the Nörlund matrix on the space of bounded variation sequences in [Eurasian J. Sci. Eng. 3, No. 2, 111--120 (2017; \url{doi:10.23918/eajse.v3i2p111})]. In this article, we define the new spaces \(b s(N^t)\) and \(c s(N^t)\) and examine the domain of the Nörlund mean on \(bs\) and \(cs\), which are bounded and convergent series, respectively. We also examine their inclusion relations. We define norms over them and investigate whether these new spaces are Banach spaces. Finally, we determine their \(\alpha\)-, \(\beta\)-, \(\gamma\)-duals, and characterize the matrix transformations on and into this space.
Mathematics Subject Classification ID: 40G05
Mathematics Subject Classification ID: 46A45
zbMATH DE Number: 6994871
zbMATH Keywords: Nörlund mean
zbMATH Keywords: Nörlund transforms
zbMATH Keywords: \(\alpha\)-dual
zbMATH Keywords: \(\beta\)-dual
zbMATH Keywords: \(\gamma\)-dual
zbMATH Keywords: matrix transformations
MaRDI profile type: Publication
full work available at URL: math6110268
OpenAlex ID: W2901742248
cites work: Q4195411
cites work: Q3050957
cites work: Q4493038
cites work: On Some Euler Sequence Spaces of Nonabsolute Type
cites work: Q5799502
cites work: Some new sequence spaces derived by the domain of generalized difference matrix
cites work: ON THE σ(A)SUMMABILITY AND σ(A)CORE
cites work: Some paranormed Riesz sequence spaces of non-absolute type
cites work: Q2996646
cites work: Domain of the double sequential band matrix in the classical sequence spaces
cites work: Almost convergence and double sequential band matrix
cites work: Domain of the double sequential band matrix in the spaces of convergent and null sequences
cites work: Paranormed sequence space of non-absolute type founded using generalized difference matrix
cites work: A study on topological and geometrical characteristics of new Banach sequence spaces
cites work: A different look for paranormed Riesz sequence space derived by Fibonacci matrix
cites work: On the Riesz almost convergent sequences space
cites work: The spaces of Cesàro almost convergent sequences and core theorems
cites work: Some new inequalities related to the invariant means and uniformly bounded function sequences
cites work: A Class of Statistical and σ-Conservative Matrices
cites work: On the statistical and σ-cores
cites work: INFINITE MATRICES AND σ(A)-CORE
cites work: On the paranormed Riesz sequence spaces of non-absolute type
cites work: Matrix transformations between sequence spaces of generalized weighted means.
cites work: On the new sequence spaces which include the spaces \(c_0\) and \(c\)
cites work: Some new paranormed sequence spaces.
cites work: Some new difference sequence spaces
cites work: Q5703654
cites work: Q3023739
cites work: On the spaces of Nörlund almost null and Nörlund almost convergent sequences
cites work: On the paranormed Nörlund sequence space of nonabsolute type
cites work: Domain of the Nörlund matrix in some of Maddox's spaces
cites work: Some multiplication theorems for the Nörlund mean
cites work: The inverse Nörlund mean
cites work: A contribution to the theory of divergent sequences
cites work: Certain topological properties and duals of the domain of a triangle matrix in a sequence space
cites work: Matrixtransformationen von Folgenräumen. Eine Ergebnisübersicht
cites work: Almost-conservative matrix transformations
cites work: Q3357625
DOI: 10.3390/MATH6110268
description: scientific article; zbMATH DE number 6994871