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1

Difference sequence spaces defined by Musielak-Orlicz function

Sharma Sunil K., Anuchaivong Patchalai, Sharma Rohit

Journal of Mathematics and Applications

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2021

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Vol. 44

107--117

EN

The purpose of this paper is to introduce sequence spaces [ wzór ]θ. We also examine some topological properties and prove some inclusion relations between these spaces.

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

Asymptotically lacunary statistical equivalence of double sequences of sets

Nuray F, Patterson R. F., Dündar E.

Demonstratio Mathematica

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2016

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Vol. 49, nr 2

183--196

EN

The concepts of Wijsman asymptotically equivalence, Wijsman asymptotically statistically equivalence, Wijsman asymptotically lacunary equivalence and Wijsman asymptotically lacunary statistical equivalence for sequences of sets were studied by Ulusu and Nuray [24]. In this paper, we get analogous results for double sequences of sets.

4

The random of lacunary statistical on χ2 over p-metric spaces defined by Musielak

Subramanian N., Babu R., Thirunavukkarasu P.

Journal of Mathematics and Applications

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2015

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Vol. 38

133--150

EN

Mursaleen introduced the concepts of statistical convergence in random 2-normed spaces. Recently Mohiuddine and Aiyup defined the notion of lacunary statistical convergence and lacunary statistical Cauchy in random 2-normed spaces. In this paper, we define and study the notion of lacunary statistical convergence and lacunary of statistical Cauchy sequences in random on χ2 over p- metric spaces dfined by Musielak and prove some theorems which generalizes Mohiuddine and Aiyup results.

5

On some new sequence spaces and statistical convergence methods for double sequences

Belen C., Yildirim M.

Demonstratio Mathematica

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2014

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Vol. 47, nr 3

627--637

EN

In this paper, we introduce some new double sequence spaces with respect to an Orlicz function and define two new convergence methods related to the concepts of statistical convergence and lacunary statistical convergence for double sequences. We also present some inclusion theorems for our newly defined sequence spaces and statistical convergence methods.

6

On some new quasi almost ∆m-lacunary strongly P-convergent double sequences defined by Orlicz functions

Khan V. A., Tabassum S.

Journal of Mathematics and Applications

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2011

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Vol. 34

45--52

EN

The idea of quasi almost P-convergent sequences defined as [...] was introduced by V.A.Khan and Q.M.D.Lohani [Mathematicki Vesnik, (60), 95-100 (2008)]. In this paper we introduce a new concept for quasi almost ∆m-lacunary strongly P-convergent double sequences defined by Orlicz function and give inclusion relations.

7

Lacunary p-absolutely summable sequences of fuzzy real numbers

Dutta A J

Fasciculi Mathematici

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2011

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Nr 46

57--64

EN

In this paper we have introduced the sequence space (lp)F0. We have established a relation between (lp)F0 and Ces(p). We have studied some algebraic properties like solidness, symmetricness, convergence free and provided some inclusion results.

8

On Lacunary strong σ-convergence with respect to a sequence of φ-fuctions

Başarir M.

Fasciculi Mathematici

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2010

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Nr 43

19-32

EN

In this paper, we introduce some new sequence spaces combining with lacunary sequence, σ-convergence, a sequence of φ-functions and a sequence of modulus functions. We establish some inclusion relations between these spaces under some conditions. Also we studied connections between lacunary (A, φk, σ )-statistically convergence with these spaces.

9

On lacunary generalized difference sequence spaces defined by Orlicz functions in a seminormed space and delta m/q-lacunary statistical convergence

Bhardwaj V., Bala I.

Demonstratio Mathematica

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2008

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Vol. 41, nr 2

415-424

EN

The main purpose of this paper is to introduce a new concept of [...]-lacunary statistical convergence. It is shown that if a sequence is [...]-lacunary strongly summable with index p with respect to an Orlicz function M then it is A [...]-lacunary statistically convergent and that the concepts of [...]-lacunary strong summability with index p with respect to an Orlicz function M and [...]-lacunary statistical convergence are equivalent on [...]-bounded sequences. The composite space no [...] using composite Orlicz function Mv has also been introduced. It is also shown that if q is total, then every [...] method is consistent with the W[...] method. Our results generalize and unify the corresponding earlier results of Freedman et al. [5], Tripathy et al. [17, 18, 19] and, Bhardwaj and Singh [1].

10

Lacunary strong Ap-convergence with respect to a modulus

Bilgin T.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2001

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[Z] 41

51-57

EN

The definition of lacunary strong A-convergence with respect to a modulus is extended to a definition of lacunary strong Ap-convergence with respect to a modulus when p = (p_i) is a real sequence with positive terms. We study some connections between lacunary strong Ap-convergence with respect to a modulus and lacunary A-statistical convergence.