Lacunary Sequence Spaces Research Articles

A Note on Lacunary Sequence Spaces of Fractional Difference Operator of Orderα,β

In the present paper, we defined lacunary sequence spaces of fractional difference operator of orderα,βovern-normed spaces via Musielak-Orlicz functionM=Ik. Our aim in this paper is to study some topological properties and inclusion relation between the spacesI−NαβA,M,u,θ,Δγ,·,⋯,·0,I−NαβA,M,u,θ,Δγ,·,⋯,·, andI−NαβA,M,u,θ,Δγ,·,⋯,·∞.

Sequence spaces defined via Euler method and matrix transformations

A blend of matrix summability and Euler summability transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties of this space and finally, some inclusion relations are presented.

Sequence spaces defined via Euler method and matrix transformations

A blend of matrix summability and Euler summability transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties of this space and finally, some inclusion relations are presented.

Orlicz lacunary sequence spaces of 𝑙-fractional difference operators

Abstract 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.

Applications of double lacunary sequences to n-norm

Abstract In the present paper we define some classes of double lacunary sequence spaces over n-normed spaces by means of a Musielak- Orlicz function. We study some relevant algebraic and topological properties. Further some inclusion relation among the classes are also examined.

$$\mu $$ μ -statistical convergent double lacunary sequence spaces

In the present paper we introduce $$\mu $$ -statistical convergent double lacunary sequence spaces defined by a sequence of Orlicz function $$\mathcal {M } = (M_{kl})$$ over $$n$$ -normed spaces. We also make an effort to study some topological properties and inclusion relations between these spaces.

Some Lacunary Sequence Spaces of Invariant Means Defined by Musielak-Orlicz Functions

Some Lacunary Sequence Spaces of Invariant Means Defined by Musielak-Orlicz Functions

Some Lacunary Sequence Spaces of Invariant Means Defined by Musielak-Orlicz Functions on 2-Norm Space

The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of sequences of Musielak-Orlicz functions, invariant means and lacunary convergence on 2-norm space. We establish some inclusion relations between these spaces under some conditions.

On two-valued measure and double statistical convergence in 2-normed spaces

In this paper we introduce some new double difference lacunary sequence spaces using Orlicz functions, generalized double difference sequences and a two-valued measure μ in 2-normed spaces, and we also examine some of their properties.

Double lacunary sequence spaces of double sequence of interval numbers

In this paper we introduce the concepts of double lacunary strongly convergence and double lacunary statistical convergence of double interval numbers. We prove some inclusion relations and study some of their properties.

Some Geometric Properties of Lacunary Sequence Spaces Related to Fixed Point Property

The main purpose of this paper is considering the lacunary sequence spaces defined by Karakaya (2007), by proving the property (β) and Uniform Opial property.

On Some Double Lacunary Sequence Spaces of Fuzzy Numbers

In this paper we introduce a new concept for lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space of fuzzy numbers. We also show that if a sequence is lacunary strong Pconvergence with respect to an Orlicz function then it is S θ r s (F) -convergent.

On some double almost lacunary sequence spaces defined by Orlicz functions

In this paper we introduce a new concept for almost lacunary strong P-convergent with respect to an Orlicz function and examine some properties of the resulting sequence space. We also introduce and study almost lacunary statistical convergence for double sequences and we shall also present some inclusion theorems.