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2 Journal of Applied Analysis

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

Singh Uday Pratap, Jasrotia Swati, Raj Kuldip

Journal of Applied Analysis

2023

Vol. 29, nr 2

229--238

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.

Orlicz lacunary sequence spaces of l-fractional difference operators

Raj Kuldip, Saini Kavita, Choudhary Anu

Journal of Applied Analysis

2020

Vol. 26, nr 2

173--183

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.