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1
Certain aspects of J-statistical supremum and J-statistical infimum of real-valued sequences
Choudhury Chiranjib
Journal of Applied Analysis
|
2023
|
Vol. 29, nr 2
305--312
EN
Over the last few years, numerous researchers have contributed significantly to summability theory by connecting various notions of convergence concepts of sequences. In this paper, we introduce the concepts of J-statistical supremum and J-statistical infimum of a real-valued sequence and study some fundamental features of the newly introduced notions.We also introduce the concept of J-statistical monotonicity and establish the condition under which an J-statistical monotonic sequence is J-statistical convergent. We end up giving a necessary and a sufficient condition for the J-statistical convergence of a real-valued sequence.
2
Content available remote On statistical convergence in quasi-metric spaces
İlkhan Merve, Kara Emrah Evren
Demonstratio Mathematica
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2019
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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.
3
Deferred weighted A-statistical convergence based upon the (p,q)-Lagrange polynomials and its applications to approximation theorems
Srivastava H. M., Jena B. B., Paikray S. K., Misra U. K.
Journal of Applied Analysis
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2018
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Vol. 24, nr 1
1--16
EN
Recently, the notion of positive linear operators by means of basic (or q-) Lagrange polynomials and A-statistical convergence was introduced and studied in [M. Mursaleen, A. Khan, H. M. Srivastava and K. S. Nisar, Operators constructed by means of q-Lagrange polynomials and A-statistical approximation, Appl. Math. Comput. 219 2013, 12, 6911-6918]. In our present investigation, we introduce a certain deferred weighted A-statistical convergence in order to establish some Korovkin-type approximation theorems associated with the functions 1, t and t2 defined on a Banach space C[0,1] for a sequence of (presumably new) positive linear operators based upon (p,q)-Lagrange polynomials. Furthermore, we investigate the deferred weighted A-statistical rates for the same set of functions with the help of the modulus of continuity and the elements of the Lipschitz class. We also consider a number of interesting special cases and illustrative examples in support of our definitions and of the results which are presented in this paper.
4
On statistically lq-complete and c0s in measure convergences of sequences of measurable functions
Papanastasiou N., Papachristodoulos C., Dimitriou X.
Journal of Applied Analysis
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2016
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Vol. 22, nr 2
163--168
EN
We introduce and study s-lq-complete and c0s-μ convergences, and we obtain a new result regarding statistical convergences of sequences of measurable functions.
5
Content available remote Ideal convergence generated by double summability methods
Connor J.
Demonstratio Mathematica
|
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.
6
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
|
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.
7
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
|
2015
|
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.
8
Content available remote On some new sequence spaces and statistical convergence methods for double sequences
Belen C., Yildirim M.
Demonstratio Mathematica
|
2014
|
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.
9
Content available remote Multiplier sequence spaces of fuzzy numbers defined by a Musielak-Orlicz function
Raj K., Gupta A.
Journal of Mathematics and Applications
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2012
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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.
10
Content available remote Statistically convergent difference double sequence spaces defined by Orlicz function
Sarma B.
Fasciculi Mathematici
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2012
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Nr 49
137--144
EN
In this article we introduce some statistically convergent difference double sequence spaces defined by Orlicz function. Completeness of the spaces will be proved. We study some of their other properties like solidness, symmetricity etc. and prove some inclusion results.
11
Content available remote Statistical approximation in multivariate modular function spaces
Belen C., Yildirim M.
Commentationes Mathematicae
|
2011
|
Vol. 51, [Z] 1
39-53
EN
In this paper, using the concept of A-statistical convergence we prove a Korovkin type approximation theorem in multivariate modular function spaces. Furthermore, giving an example via bivariate operators of Kantorovich type, it is shown that our theorem is stronger than its classical case.
12
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.
13
Content available remote Statistically convergent difference sequence spaces of fuzzy real numbers
Tripathy B. C., Das P. C.
Fasciculi Mathematici
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2008
|
Nr 39
97-112
EN
In this article we introduce the notion of statistical convergence difference sequences of fuzzy real numbers, cF(A). We study some properties of the statistically convergent and statistically null difference sequence spaces of fuzzy real numbers, like completeness, solidness, sequence algebra, symmetricity, convergence free, nowhere denseness and some inclusion results.
14
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.
15
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].
16
Content available remote Statistical convergence on composite vector valued sequence space
Basu A., Srivastava P. D.
Journal of Mathematics and Applications
|
2007
|
Vol. 29
75-90
EN
In this paper, we have defined the idea of statistical convergence and statistically Cauchy sequence over the generalized class of composite vector valued sequence space F(Ek, f). The class F(Ek, f) is in-troduced and discussed by Ghosh and Srivastava [7], where F is a normal paranormed sequence space, Ek's are Banach spaces and f is a modulus function. We have established some results of Fridy, Connor and Rath and Tripathy, such as, decomposition of statistically convergent sequences, equivalence of statistical convergence and statistical Cauchy convergence and sequentially completeness of the space of bounded statistically con-vergent sequences of F [E, f].
17
Content available remote Strongly (Vσ,θ, q] - summable sequences defined by Orlicz functions
Altin Y., Tripathy B. Ch., Isik M., Et M.
Fasciculi Mathematici
|
2005
|
Nr 36
15-26
EN
The purpose of this paper is to introduce the space of sequences those are strongly -summable with respect to an Orlicz function. We give some relations related to these sequence spaces. We also show that the spaces may be represented as a space.
18
Content available remote Lacunary strong Ap-convergence with respect to a modulus
Bilgin T.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2001
|
[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.
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