On generalized sequence spaces via modulus function
TL;DR: In this article, the authors introduce and study the concept of lacunary strongly (A, ϕ)-convergence with respect to a modulus function and examine some properties of these sequence spaces.
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Abstract: In this paper, we introduce and study the concept of lacunary strongly (A, ϕ)-convergence with respect to a modulus function and lacunary (A, ϕ)-statistical convergence and examine some properties of these sequence spaces. We establish some connections between lacunary strongly (A, ϕ)-convergence and lacunary (A, ϕ)-statistical convergence. MSC: Primary 40H05; secondary 40C05
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Citations
Deferred statistical convergence of order α in topological groups
Hacer Sengul,Mikail Et,Huseyin Cakalli +2 more
- 06 Dec 2019
TL;DR: In this paper, the concept of deferred statistical convergence of order α is generalized to topological groups and some inclusion relations between the set of all statistically convergent sequences of order in topology groups and the set for all deferred statistically convergences of order ρ in topological group are given.
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Some Difference Paranormed Sequence Spaces over n-normed Spaces Defined by a Musielak-Orlicz Function
TL;DR: In this paper, the authors introduce difference paranormed sequence spaces, which are de-fineed by a Musielak-Orlicz function over n-normed spaces.
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Some new lacunary I-convergent sequences of fuzzy real numbers
Adem Kilicmen,Stuti Borgohain +1 more
TL;DR: In this paper, some strongly almost lacunary I-convergent generalized sequence spaces of fuzzy real numbers defined by an Orlicz function are introduced and studied their diff?erent properties.
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Note on $f_\lambda$-statistical convergence
Stuti Borgohain,Ekrem Savaş +1 more
TL;DR: In this paper, the authors investigated the relation between the sumability and statistical convergence of moduli and found some results related to statistical convergence with respect to the density of modulus.
Applications of fractional difference operators for new version of Brudno-Mazur Orlicz bounded consistency theorem
Kuldip Raj,K. K. Choudhary,Mohammad Mursaleen +2 more
TL;DR: The modulus lacunary fractional difference statistical convergence of fractional difference sequences and matrices is equivalent to the modulus $\mathcal{A}-$lacunary statistical convergence.
References
On statistical convergence
TL;DR: In this article, it is shown that Statistical convergence cannot be included by any matrix metbod. And two Tauberian theorems are proved: one uses the Tauberians condition Axi, = 0(1/Ar), which is shown to be ''best possible,\" and the other is concerned with gap sequences.
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The Integrability of Certain Functions and Related Summability Methods
TL;DR: The Integrability of Certain Functions and Related Summability Methods as discussed by the authors is a seminal work in the field of algebraic geometry, and it has been used extensively in many applications.
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