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2021, Proyecciones (Antofagasta)
In this paper we investigate the notion of I-statistical ϕ-convergence and introduce IS-ϕ limit points and IS-ϕ cluster points of real number sequence and also studied some of its basic properties.
Proyecciones (Antofagasta), 2019
In this paper we have extended the notion of λ-statistical limit points of real sequences to I λ-statistical limit points and studied some basic properties of the set of all I λ-statistical limit points and I λ-statistical cluster points of real sequences including their interrelationship. Then we have established I λ-statistical analogue of the monotone sequence theorem. Also introducing additive property of I λ-density zero sets we have established its relationship with I λ-statistical convergence. Keywords I λ-statistical convergence, I λ-statistical limit point, I λ-statistical cluster point, I λ-density, I λ-statistical boundedness.
Malaya Journal of Matematik, 2021
In this paper we have extended the notion of λ -statistical limit points of real sequences to I λ -statistical limit points and studied some basic properties of the set of all I λ -statistical limit points and I λ -statistical cluster points of real sequences including their interrelationship. Then we have established I λ -statistical analogue of the monotone sequence theorem. Also introducing additive property of I λ -density zero sets we have established its relationship with I λ -statistical convergence. I λ -statistical convergence, I λ -statistical limit point, I λ -statistical cluster point, I λ -density, I λ -statistical boundedness.
2011
In this paper we develop a method suggested by Pehlivan and Mamedov [29]. We study some problems concerning the set of -statistical cluster points (briefly, -s.c. points) in finite-dimensional Banach spaces. We also give some results related to the set of -statistical cluster points x . AMS Subject Classifications: 40A05, 46A45.
arXiv: Functional Analysis, 2018
In this paper we have extended the notion of statistical limit point as introduced by Fridy[8] to I-statistical limit point of sequences of real numbers and studied some basic properties of the set of all I-statistical limit points and I-statistical cluster points of real sequences.
2017
In this paper we are concerned with the recent summability notion of I-statistically pre-Cauchy real double sequences in line of Das et. al. [6] as a generalization of I-statistical convergence. Here we introduce the notion of double I-natural density and present some interesting properties of I-statistically pre-Cauchy double sequences of real numbers. Also in this paper we investigate the notion of I-statistical cluster point of double sequences in finite dimensional normed space.
Filomat
In this paper we have extended the concepts of I-limit superior and I-limit inferior to I-statistical limit superior and I-statistical limit inferior and studied some of their properties for sequence of real numbers.
2013
The object of this present paper is to dene and study generalised statistical convergence for the sequences in any locally convex Hausdorff space X whose topology is determined by a set Q of continuous seminorms q and their relation with the nearly convergent sequence space using a bounded modulus function along with regular and almost positive method.
Ukrainian Mathematical Journal, 2014
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
Taiwanese J. Math, 2007
P. Kostyrko et al. [12] introduced the concept of I-convergence of sequences in a metric space and studied some properties of this convergence. Note that I-convergence is an interesting generalization of statistical convergence. The concept of statistical convergence was introduced by ...
Science in China Series A: Mathematics, 2008
The purpose of this paper is to unify various kinds of statistical convergence by statistical measure convergence and to present Jordan decomposition of finitely additive measures. It is done through dealing with the most generalized statistical convergence-ideal convergence by applying geometric functional analysis and Banach space theory. We first show that for each type of ideal I(⊂ 2 N ) convergence, there exists a set S of statistical measures such that the measure S-convergence is equivalent to the statistical convergence. To search for Jordan decomposition of measures of statistical type, we show that the subspace X I ≡ span{χ A : A ∈ I} is an ideal of the space ℓ ∞ in the sense of Banach lattice, hence the quotient space ℓ ∞ /X I is isometric to a C (K ) space. We then prove that a statistical measure has a Jordan decomposition if and only if its corresponding functional is norm-attaining on ℓ ∞ , and which in turn induces an approximate null-ideal preserved Jordan decomposition theorem of finitely additive measures. Finally, we show this characterization and the approximate decomposition theorem are true for finitely additive measures defined on a general measurable space. n j=1 χ S (j) = 0 is said to be a statistically null set, or simply, a null set if there is no confusion arise, where χ A denotes the characteristic function of a set A. On one hand, properties of statistical convergence has been studied in many pure and applied mathematical fields (see, for example, ). On the other hand, the notion of statistical convergence has been generalized in different ways. The original notion was introduced for X = R, and there are dozens of its generalizations. Generally speaking, this notion was extended in two directions: One is to discuss statistical convergence in more general spaces, for example, locally convex spaces , including Banach spaces with the weak topologies , and general topological spaces . The other is to consider generalized notions defined by various limit processes, for example, A-statistical convergence [6], lacunary statistical convergence . The most general notion of statistical convergence is ideal (or filter) convergence .
Journal of Mathematical Analysis and Applications, 1996
Ž . This article extends the concept of a statistical limit cluster point of a sequence Ž .
International Journal of ADVANCED AND APPLIED SCIENCES
In this paper, we introduce the concepts of ∫ Γ 2 statistical convergence and strongly ∫ Γ 2 of real numbers. It is also shown that Γ 2 statistical convergence and strongly ∫ Γ 2 are equivalent for analytic sequences of real numbers. We introduce certain new double sequence spaces of ∫ Γ 2 of fuzzy real numbers defined by − convergence using sequences of Musielak-Orlicz functions and also study some basic topological and algebraic properties of these spaces, investigate the inclusion relations between these spaces.
2004
In the paper [5] the concept of I-convergence is introduced. This concept is a generalization of the statistical convergence. In this paper some notions and results from the statistical convergence are extended to the Iconvergence.
Filomat, 2014
In this paper we study the concepts of Wijsman I-statistical convergence, Wijsman I-lacunary statistical convergence and Wijsman strongly I-lacunary convergence of sequences of sets and investigate the relationship between them.
Czechoslovak Mathematical Journal, 2000
In this paper we study the set of statistical cluster points of sequences in mdimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in m-dimensional spaces too. We also define a notion of Γ-statistical convergence. A sequence x is Γ-statistically convergent to a set C if C is a minimal closed set such that for every ε > 0 the set {k : (C, x k ) ε} has density zero. It is shown that every statistically bounded sequence is Γ-statistically convergent. Moreover if a sequence is Γ-statistically convergent then the limit set is a set of statistical cluster points.
Journal of Inequalities and Applications, 2013
In this paper we study the notion of statistical ( A , λ ) -summability, which is a generalization of statistical A-summability. We study here many other related concepts and its relations with statistical convergence and λ-statistical convergence and provide some interesting examples.
arXiv: Functional Analysis, 2019
The objective of this paper is to introduce the notion of generalized almost statistical (briefly, GAS) convergence of bounded real sequences, which generalizes the notion of almost convergence as well as statistical convergence of bounded real sequences. As a special kind of Banach limit functional, we also introduce the concept of Banach statistical limit functional and the notion of GAS convergence mainly depends on the existence of Banach statistical limit functional. We prove the existence of Banach statistical limit functional. Then we have shown the existence of a GAS convergent sequence, which is neither statistical convergent nor almost convergent. Also, some topological properties of the space of all GAS convergent sequences are investigated.
Applied Mathematics and Computation, 2009
We investigate the structure of the set of all statistical limit points of a double sequence and prove certain results, mainly showing that this set can be characterized as a F r -set.
Mathematical and Computer Modelling, 2009
A real-valued finitely additive measure µ on N is said to be a measure of statistical type provided µ(k) = 0 for all singletons {k}. Applying the classical representation theorem of finitely additive measures with totally bounded variation, we first present a short proof of the representation theorem of statistical measures. As its application, we show that every kind of statistical convergence is just a type of measure convergence with respect to a specific class of statistical measures.
Applied Mathematics E Notes, 2013
The aim of the present paper is to give some properties of A-statistical convergence of sequences. We give de…nition of A-statistical monotonicity, upper and lower peak points of sequences. The relation between these concepts and A-statistical monotonicity is investigated. Also, some results given in [11] are generalized.
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