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1

Linear isomorphic spaces of Cesàro-Nörlund operator, their duals and matrix transformations

Singh Uday Pratap, Jasrotia Swati, Raj Kuldip

Journal of Applied Analysis

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2023

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Vol. 29, nr 2

229--238

EN

In this article, we introduce and study sequence spaces of Cesàro-Nörlund operators of order n associated with a sequence of Orlicz functions.We obtain some topological properties and Schauder basis of these sequence spaces.Moreover, we compute the α-, β- and γ-duals and the matrix transformations of these newly formed sequence spaces. Finally, we prove that these sequence spaces are of Banach-Saks type p and have a weak fixed-point property.

2

Orlicz lacunary sequence spaces of l-fractional difference operators

Raj Kuldip, Saini Kavita, Choudhary Anu

Journal of Applied Analysis

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2020

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Vol. 26, nr 2

173--183

EN

Recently, S. K. Mahato and P.D. Srivastava [A class of sequence spaces defined by l-fractional difference operator, preprint (2018), http://arxiv.org/abs/1806.10383] studied l-fractional difference sequence spaces. In this article, we intend to make a new approach to introduce and study some lambda l-fractional convergent, lambda l-fractional null and lambda l-fractional bounded sequences over n-normed spaces. Various algebraic and topological properties of these newly formed sequence spaces have been explored, and some inclusion relations concerning these spaces are also established. Finally, some characterizations of the newly formed sequence spaces are given.

3

Solvability of certain sequence spaces inclusion equations with operators

Malafosse B. de

Demonstratio Mathematica

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2013

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Vol. 46, nr 2

299--314

EN

In this paper, we deal with sequence spaces inclusion equations (SSIE), which are determined by an inclusion where each term is a sum or a sum of products of sets of the form a(T) and f(x)(T) where f maps U+ to itself, and (...), the sequence x is the unknown and T is a given triangle. Here, we determine the set of all sequences x with positive entries such that (…) and (…) where (...). We are led to study, among other things, the inclusion equations (…) and (…) where (…) is the operator of first differences defined by (…) for (…) with (…). The first (SSIE) leads to determine the set of all sequences x such that (…) and (…) implies (…). These results generalize some of the results given in [1].

4

On the degree of approximation of continuous functions by matrix means related to partial sums of a Fourier series

Krasniqi X. Z.

Commentationes Mathematicae

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2012

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Vol. 52, [Z] 2

207--215

EN

In this paper we generalize some results on the degree of approximation of continuous functions by matrix means related to partial sums of a Fourier series, obtained previously by some other authors (please consult references cited in this paper).

5

Sets of sequences that are strongly r-bounded and matrix transformations between these sets

Malafosse B. de

Demonstratio Mathematica

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2003

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Vol. 36, nr 1

155--171

EN

In this paper we are giving some new properties of the operator of first-difference mapping a space sr into itself and we are dealing with the spaces sr(A h) and sr((A+) ). Next are given some properties of the spaces wr^(A,//),