A-statistical convergence and A-statistical monotonicity

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.

2008

This paper presents new definitions which are a natural combination of the definition for asymptotically equivalence ∆−lacunary statistically convergence. Using this definitions we have proved the Sθ (∆)-asymptotically equivalence analogues theorems of [5] and [6].

Advances in Difference Equations, 2013

In this paper we define the λ(u)-statistical convergence that generalizes, in a certain sense, the notion of λ-statistical convergence. We find some relations with sets of sequences which are related to the notion of strong convergence. MSC: 40A05; 40H05

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.

Journal of the Indonesian Mathematical Society

By using modulus functions, we have obtained a generalization of statistical convergence of asymptotically equivalent sequences, a new non-matrix convergence method, which is intermediate between the ordinary convergence and the statistical convergence. Further, we have examined some inclusion relations related to this concept.

Filomat, 2008

This paper presents new definitions which are a natural combination of the definition for asymptotically equivalence ∆−lacunary statistically convergence. Using this definitions we have proved the S L θ (∆)-asymptotically equivalence analogues theorems of [5] and .

Miskolc Mathematical Notes, 2017

In this paper we define generalized statistical convergence for sequences of sets of order˛; 0 <˛Ä 1 in sense of Wijsman and study some basic properties of this concept.

2005

A lacunary sequence is an increasing integer sequence θ = (kr) such that k0 =0, kr −kr−1 → ∞ as r → ∞. A sequence x is called S θ (∆ m)− convergent to L provided that for each ε > 0, limr(kr − kr−1) −1 {the number of kr−1 < k ≤ kr : |∆ m x k −L| ≥ ε} = 0, where ∆ m x k = ∆ m−1 x k − ∆ m−1 x k+1. The purpose of this paper is to introduce the concept of ∆ m − lacunary statistical convergence and ∆ m-lacunary strongly convergence and examine some properties of these sequence spaces. We establish some connections between ∆ m-lacunary strongly convergence and ∆ m-lacunary statistical convergence. It is shown that if a sequence is ∆ m-lacunary strongly convergent then it is ∆ m-lacunary statistically convergent. We also show that the space S θ (∆ m) may be represented as a [f, p, θ](∆ m) space.

Filomat, 2006

This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent, λ-statistical convergence and σ-convergence. Two nonnegative sequences [x] and [y] are said to be S σ,λ-asymptotically equivalent of multiple L provided that for every > 0 lim n 1 λn k ∈ In : x σ k (m) y σ k (m) − L ≥ = 0 uniformly in m = 1, 2, 3, .... (denoted by x S σ,λ ∼ y) and simply S σ,λasymptotically equivalent, if L = 1. Using this definition we shall prove S σ,λ-asymptotically equivalent analogues of Mursaleen's theorems in [8]. 1991 Mathematics Subject Classification. 40C05.

Journal of Universal Mathematics Vol.4 No.1 pp.34-41 (2021), 2021

In this paper, we are going to define λ-statistical supremum and λ-statistical infimum for real valued sequencex = (xn) n∈N by considering λ-statistical upper and lower bounds, respectively. After giving some basic properties of these new notations, then we will give a necessary and sufficient condition for to existance of λ-statistical convergence of the real valued sequence.

A real valued function $f$ defined on a subset $E$ of $\textbf{R}$, the set of real numbers, is statistically upward continuous if it preserves statistically upward half quasi-Cauchy sequences, is statistically downward continuous if it preserves statistically downward half quasi-Cauchy sequences; and a subset $E$ of $\textbf{R}$, is statistically upward compact if any sequence of points in $E$ has a statistically upward half quasi-Cauchy subsequence, is statistically downward compact if any sequence of points in $E$ has a statistically downward half quasi-Cauchy subsequence where a sequence $(x_{n})$ of points in $\textbf{R}$ is called statistically upward half quasi-Cauchy if \[ \lim_{n\rightarrow\infty}\frac{1}{n}|\{k\leq n: x_{k}-x_{k+1}\geq \varepsilon\}|=0 \] is statistically downward half quasi-Cauchy if \[ \lim_{n\rightarrow\infty}\frac{1}{n}|\{k\leq n: x_{k+1}-x_{k}\geq \varepsilon\}|=0 \] for every $\varepsilon&gt;0$. We investigate statistically upward continuity, statist...

Chaos, Solitons & Fractals, 2009

We consider the set S of sequences of positive real numbers in the context of statistical convergence/divergence and show that some subclasses of S have certain nice selection and game-theoretic properties.

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.

2006

This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent, λ-statistical convergence and σ-convergence. Two nonnegative sequences [x] and [y] are said to be S σ,λ -asymptotically equivalent of multiple L provided that for every > 0 lim n 1 λn k ∈ In : x σ k (m) y σ k (m) − L ≥ = 0 uniformly in m = 1, 2, 3, .... (denoted by x S σ,λ

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.