A-Statistical Supremum-Infimum and A-Statistical Convergence

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.

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.

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.

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.

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 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.

Journal of Mathematical Analysis and Applications, 1996

Ž . This article extends the concept of a statistical limit cluster point of a sequence Ž .

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.

Journal of Mathematical Analysis and Applications, 2007

Let I ⊂ P(N) stand for an ideal containing finite sets. We discuss various kinds of statistical convergence and I-convergence for sequences of functions with values in R or in a metric space. For real valued measurable functions defined on a measure space (X, M, μ), we obtain a statistical version of the Egorov theorem (when μ(X) < ∞). We show that, in its assertion, equi-statistical convergence on a big set cannot be replaced by uniform statistical convergence. Also, we consider statistical convergence in measure and I-convergence in measure, with some consequences of the Riesz theorem. We prove that outer and inner statistical convergences in measure (for sequences of measurable functions) are equivalent if the measure is finite.

Acta Mathematica Hungarica, 2007

We introduce the concept of the statistical limit (at ∞) of a measurable function in several variables and recall the concept of the statistical convergence of a multiple sequence. Then we extend a classical theorem of Schoenberg (which characterizes statistical convergence) from single to multiple sequences, and prove an analogous theorem on statistical limit. These theorems even may be extended to vector-valued sequences or functions, respectively.