Some Generalized Difference Sequence Spaces Defined by Ideal Convergence and Musielak-Orlicz Function

Bakery, Awad A.; Mohamed, Elsayed A. E.; Ahmed, Mohamed Alamin

doi:10.1155/2013/972363

Cited by 2 publications

(1 citation statement)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For more details and linked concept, we refer to [18][19][20][21][22][23][24][25][26]. In [27,28], Gähler introduced a gorgeous theory of 2-normed and -normed spaces in the 1960s; we have studied these subjects and constructed some sequence spaces defined by ideal convergence in -normed spaces [29,30]. Another important alternative of statistical convergence is the notion of lacunary statistical convergence introduced by Fridy and Orhan [31].…”

Section: Introductionmentioning

confidence: 99%

On Lacunary Mean Ideal Convergence in Generalized Randomn-Normed Spaces

Bakery

Mohammed

2014

Abstract and Applied Analysis

Self Cite

View full text Add to dashboard Cite

An idealIis a hereditary and additive family of subsets of positive integersℕ. In this paper, we will introduce the concept of generalized randomn-normed space as an extension of randomn-normed space. Also, we study the concept of lacunary mean (L)-ideal convergence andL-ideal Cauchy for sequences of complex numbers in the generalized randomn-norm. We introduceIL-limit points andIL-cluster points. Furthermore, Cauchy andIL-Cauchy sequences in this construction are given. Finally, we find relations among these concepts.

show abstract

Section: Introductionmentioning

confidence: 99%

On Lacunary Mean Ideal Convergence in Generalized Randomn-Normed Spaces

Bakery

Mohammed

2014

Abstract and Applied Analysis

Self Cite

View full text Add to dashboard Cite

show abstract

Some New Difference Sequence Spaces of Invariant Means Defined by Ideal and Modulus Function

Kumar

Bhatia

2014

International Journal of Analysis

View full text Add to dashboard Cite

The main objective of this paper is to introduce a new kind of sequence spaces by combining the concepts of modulus function, invariant means, difference sequences, and ideal convergence. We also examine some topological properties of the resulting sequence spaces. Further, we introduce a new concept of Δ (I)-convergence and obtain a condition under which this convergence coincides with above-mentioned sequence spaces.

show abstract

Some Generalized Difference Sequence Spaces Defined by Ideal Convergence and Musielak-Orlicz Function

Abstract: In the present paper we introduced the ideal convergence of generalized difference sequence spaces combining de La Vallée-Poussin mean and Musielak-Orlicz function overn-normed spaces. We also study some topological properties and inclusion relation between these spaces.

Cited by 2 publications

References 18 publications

On Lacunary Mean Ideal Convergence in Generalized Randomn-Normed Spaces

On Lacunary Mean Ideal Convergence in Generalized Randomn-Normed Spaces

Some New Difference Sequence Spaces of Invariant Means Defined by Ideal and Modulus Function

Contact Info

Product

Resources

About