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1
Content available remote On statistical convergence in quasi-metric spaces
İlkhan Merve, Kara Emrah Evren
Demonstratio Mathematica
|
2019
|
Vol. 52, nr 1
225--236
EN
A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric in general. Quasi-metrics are a subject of comprehensive investigation both in pure and applied mathematics in areas such as in functional analysis, topology and computer science. The main purpose of this paper is to extend the convergence and Cauchy conditions in a quasi-metric space by using the notion of asymptotic density. Furthermore, some results obtained are related to completeness, compactness and precompactness in this setting using statistically Cauchy sequences.
2
Content available remote Ideal convergence generated by double summability methods
Connor J.
Demonstratio Mathematica
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2016
|
Vol. 49, nr 1
26--37
EN
The main result of this note is that if I is an ideal generated by a regular double summability matrix summability method T that is the product of two nonnegative regular matrix methods for single sequences, then I-statistical convergence and convergence in I-density are equivalent. In particular, the method T generates a density μT with the additive property (AP) and hence, the additive property for null sets (APO). The densities used to generate statistical convergence, lacunary statistical convergence, and general de la Vallée-Poussin statistical convergence are generated by these types of double summability methods. If a matrix T generates a density with the additive property then T-statistical convergence, convergence in T-density and strong T-summabilty are equivalent for bounded sequences. An example is given to show that not every regular double summability matrix generates a density with additve property for null sets.
3
Content available remote 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
Content available 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
Content available remote On some new sequence spaces and statistical convergence methods for double sequences
Belen C., Yildirim M.
Demonstratio Mathematica
|
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
Content available remote Multiplier sequence spaces of fuzzy numbers defined by a Musielak-Orlicz function
Raj K., Gupta A.
Journal of Mathematics and Applications
|
2012
|
Vol. 35
69--81
EN
In this paper we introduce some multiplier sequence spaces of fuzzy number by using a Musielak-Orlicz function ℳ = (Mk) and multiplier function u = (uk) and prove some inclusion relations between the resulting sequences spaces.
7
Content available remote On Lacunary strong σ-convergence with respect to a sequence of φ-fuctions
Başarir M.
Fasciculi Mathematici
|
2010
|
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.
8
Content available remote Strong invariant A-summability with respect to a sequence of modulus functions in seminormed space
Bhardwaj V., Bala I.
Demonstratio Mathematica
|
2008
|
Vol. 41, nr 4
869-877
EN
The object of this paper is to introduce some new strongly invariant A-summable sequence spaces defined by a sequence of modulus functions T = (fk) in a seminormed space, when A = (ank) is a non-negative regular matrix. Various algebraic and topological properties of these spaces, and some inclusion relations between these spaces have been discussed. Finally, we study some relations between ^4-invariant statisti-cal convergence and strong invariant A-summability with respect to a seąuence of modulus functions in a seminormed space.
9
Content available remote 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
|
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].
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