scholarly journals I2-lacunary strongly summability for multidimensional measurable functions

2020 ◽  
Vol 107 (121) ◽  
pp. 93-107
Author(s):  
Rabia Savaş ◽  
Richard Patterson
Keyword(s):  
Statistical Convergence ◽  
New Approach ◽  
New Methods ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence ◽  
Nontrivial Ideal

Let I2 ? P(N ? N) be a nontrivial ideal. We provide a new approach to the concept of I2-double lacunary statistical convergence and I2-lacunary strongly double summable by taking f(?,?), which is a multidimensional measurable real valued function on (1,?) ? (1,?). Additionally, we examine the relation between these two new methods.

scholarly journals Sliding window convergence and lacunary statistical convergence for measurable functions via modulus function

2018 ◽  
Vol 36 (1) ◽  
pp. 161 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Kuldip Raj
Keyword(s):  
Statistical Convergence ◽  
Sliding Window ◽  
Modulus Function ◽  
Convergence Criterion ◽  
Sequential Methods ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence

In this paper we study the concepts of sliding window convergence for real valued measurable functions dened on [0,1) via modulus function. We also establish some inclusions and consistency theorems for sequential methods along with examples. Finally, we give a Cauchy convergence criterion.

scholarly journals Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Double Sequence ◽  
Finite Measure ◽  
Measurable Space ◽  
Double Sequences ◽  
Convergence In Measure ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α -level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions.

On I-lacunary statistical convergence of weight g of sequences of sets

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5315-5322 ◽  
Author(s):  
Ekrem Savaş
Keyword(s):  
Statistical Convergence ◽  
Open Problems ◽  
New Approach ◽  
Summability Methods ◽  
Lacunary Statistical Convergence

In this paper, following a very recent and new approach of [1], we further generalize recently introduced summability methods in [13] and introduce new notions, namely, I-statistical convergence of weight 1 and I-lacunary statistical convergence of weight g, where g : N ? [0,?) is a function satisfying lim n?? g(n) = ? and n/g(n) ?? 0 as n ? ?, for sequences of sets. We mainly investigate their relationship and also make some observations about these classes. The study leaves a lot of interesting open problems.

scholarly journals On Some Further Generalizations of Strong Convergence in Probabilistic Metric Spaces Using Ideals

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Pratulananda Das ◽  
Kaustubh Dutta ◽  
Vatan Karakaya ◽  
Sanjoy Ghosal
Keyword(s):  
Strong Convergence ◽  
Metric Space ◽  
Statistical Convergence ◽  
Metric Spaces ◽  
Strong Topology ◽  
Probabilistic Metric Space ◽  
Probabilistic Metric Spaces ◽  
New Approach ◽  
Lacunary Statistical Convergence ◽  
Probabilistic Metric

Following the line of (Das et al., 2011, Savas and Das, 2011), we make a new approach in this paper to extend the notion of strong convergence and more general strong statistical convergence (Şençimen and Pehlivan, 2008) using ideals and introduce the notion of strongℐ- andℐ*-statistical convergence and two related concepts, namely, strongℐ-lacunary statistical convergence and strongℐ-λ-statistical convergence in a probabilistic metric space endowed with strong topology. We mainly investigate their interrelationship and study some of their important properties.

scholarly journals ON GENERALIZED STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES VIA IDEALS IN INTUITIONISTIC FUZZY NORMED SPACES

2021 ◽  
pp. 435
Author(s):  
Ömer Kişi
Keyword(s):  
Normed Space ◽  
Statistical Convergence ◽  
Double Sequences ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
New Methods ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Lacunary Statistical Convergence ◽  
Intuitionistic Fuzzy Normed Spaces

In this paper, we introduce the concept of I₂-lacunary statistical convergence and strongly I₂-lacunary convergence with respect to the intuitionistic fuzzy norm (μ,v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between I₂-statistical convergence in the corresponding intuitionistic fuzzy normed space.

New Methods of Technological Cooperation in Europe

1992 ◽  
Vol 6 (4) ◽  
pp. 229-238
Author(s):  
Helwig Schmied
Keyword(s):  
Basic Assumption ◽  
Research Collaboration ◽  
Management Problem ◽  
New Approach ◽  
New Methods ◽  
Technological Cooperation ◽  
Core Problem ◽  
And Robotics

This article is founded on the basic assumption that Europe taken as a whole possesses all the necessary resources to combat successfully any non-European competitor in the fields of technology, provided that it solves the management problem of organizing the coordination of those resources. At present, the author argues, they are dispersed and so underexploited. To contribute to the solution of this core problem, he sets out a new approach to research collaboration, using the example of the German–French Institute for Automation and Robotics to show ways in which HEIs can cooperate internationally to provide industry with what it needs to be truly competitive.

scholarly journals Some New Methods in the Theory of $m$-Quasi-Invariants

10.37236/1877 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
J. Bell ◽  
A. M. Garsia ◽  
N. Wallach
Keyword(s):  
Symmetric Functions ◽  
Free Module ◽  
Finitely Generated ◽  
Graded Algebras ◽  
New Approach ◽  
Elementary Symmetric Functions ◽  
New Methods ◽  
Regular Sequences

We introduce here a new approach to the study of $m$-quasi-invariants. This approach consists in representing $m$-quasi-invariants as $N^{tuples}$ of invariants. Then conditions are sought which characterize such $N^{tuples}$. We study here the case of $S_3$ $m$-quasi-invariants. This leads to an interesting free module of triplets of polynomials in the elementary symmetric functions $e_1,e_2,e_3$ which explains certain observed properties of $S_3$ $m$-quasi-invariants. We also use basic results on finitely generated graded algebras to derive some general facts about regular sequences of $S_n$ $m$-quasi-invariants

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