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2016
In this paper, statistical convergence is generalized by using regular Norlund mean N(p) where p = (pn) is a positive sequence of natural numbers. It is called statistical Norlund convergence and denoted by the symbol st-N(p). Besides convergence properties of st-N(p), some inclusion results have been given between st-N(p) convergence and strongly N(p) and statistical convergence. Also, st-N(p) and st-N(q) convergences are compared under some certain restrictions.
In this paper, the notion of N, p, qE, q summability is introduced to generalize the concept of Norlund –Euler statistical convergence. We call this new method generalized weighted Norlund-Euler statistically convergence. We will show some properties of this summability method . Mathematics Subject Classification: 40G15 Keywords: Norlund-Euler type means, generalized weighted Norlund-Euler statistical convergence, sequence spaces, Euler summability
In this paper we will define the new weighted statistically summbaility method, known as the weighted Norlund-Euler statistical convergence. We will show some properties of this method and we have proved Korovkin type theorem.
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.
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.
Abstract. In this paper we study the rate of weighted Norlund–Euler statistical convergence. We also prove the regularity of method in theorem1.1. Mathematics Subject Classification: 41A10; 40A05, 40C05 Keywords: Density; Statistical convergence; Generalized weighted Norlund–Euler statistical convergence; Sequence spaces, Euler summability
2013
The main aim of this paper is to investigate properties of statistically convergent sequences. Also, the denition of statistical mono- tonicity and upper (or lower) peak points of real valued sequences will be introduced. The interplay between the statistical convergence and these concepts are also studied. Finally, the statistically monotonicity is gener- alized by using a matrix transformation.
Applied Mathematics Letters, 2009
Two concepts-one of almost convergence and the other of statistical convergence-play a very active role in recent research on summability theory. The definition of almost convergence introduced by Lorentz [G.G. Lorentz, A contribution to theory of divergent sequences, Acta Math. 80 (1948) 167-190] originated from the concept of the Banach limit, while the statistical convergence introduced by Fast [H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951) 241-244] was defined through the concept of density. Both involve non-matrix methods of summability and they are incompatible. In this work we define two new kinds of summability methods by using these two mutually incompatible concepts of the Banach limit and of density to deal with those sequences which are statistically convergent but not almost convergent or vice versa.
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.
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 .
Abstract. We introduce the notion of weighted Norlund –Euler A-Statistical Convergence of a sequence, where A represents the nonnegative regular matrix. We also prove the Korovkin approximation theorem by using the notion of weighted Norlund-Euler A-statistical convergence. Further, we give a rate of weighted NorlundEuler A-statistical convergence.
Proceedings of the Estonian Academy of Sciences, 1998
In this article the results of Dedekind and Abel for term product of series are extended to statistically convergent series. An extension of Leibniz's test is given and Tauberian theorems are proved.
Symmetry
In this paper, we defined weighted (Eλ,q)(Cλ,1) statistical convergence. We also proved some properties of this type of statistical convergence by applying (Eλ,q)(Cλ,1) summability method. Moreover, we used (Eλ,q)(Cλ,1) summability theorem to prove Korovkin’s type approximation theorem for functions on general and symmetric intervals. We also investigated some of the results of the rate of weighted (Eλ,q)(Cλ,1) statistical convergence and studied some sequences spaces defined by Orlicz functions.
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020
The notion of deferred weighted statistical probability convergence has recently attracted the widespread attention of researchers due mainly to the fact that it is more general than the deferred weighted statistical convergence. Such concepts were introduced and studied by Srivastava et al. (Appl Anal Discrete Math, 2020). In the present work, we introduced and studied the notion of statistical probability convergence as well as statistical convergence for sequences of random variables and sequences of real numbers respectively defined over a Banach space via deferred Nörlund summability mean. We have also established a theorem presenting a connection between these two interesting notions. Moreover, based upon our proposed methods, we have proved a new Korovkin-type approximation theorem with algebraic test functions for a sequence of random variables on a Banach space and demonstrated that our theorem effectively extends and improves most (if not all) of the previously existing results (in statistical versions). Finally, an illustrative example is presented here by the generalized Meyer-König and Zeller operators of a sequence of random variables in order to demonstrate that our established theorem is stronger than its traditional and statistical versions.
Acta Scientiarum. Technology, 2013
Dois novos tipos de convergência estatística e o método de sumabilidade RESUMO. Introduzem-se e investigam-se a relação entre
FOURTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2020), 2021
In this study, we introduce and examine the concepts of Δ m −weighted statistical convergence and Δ m −weighted N, p n −summability. Also some relations between Δ m −weighted statistical convergence and Δ m −weighted N, p n −summability are given.
Journal of Applied Mathematics and Computing, 2020
In this paper, we propose to investigate a new weighted statistical convergence by applying the Nörlund-Cesáro summability method. Based upon this definition, we prove some properties of statistically convergent sequences and a kind of the Korovkin type theorems. We also study the rate of the convergence for this kind of weighted statistical convergence and a Voronovskaya type theorem. Keywords Weighted statistical convergence • Sequence spaces • Korovkin type theorem • Rate of convergence • Voronovskaya type theorem Mathematics Subject Classification 40G15 • 41A36 • 46A35 • 46A45 |K n | n if the limit exists, where the vertical bars in |K n | indicate the number of elements in the enclosed B Naim L. Braha
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.
Proyecciones (Antofagasta), 2021
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.
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 Research -GRANTHAALAYAH, 2017
In this paper, we have established some new theorems on double weighted mean statistical convergence of double sequences, which gives some new results and generalizes the some previous known results of Karakaya.
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