scholarly journals I2-uniform convergence of double sequences of functions

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1273-1281 ◽  
Author(s):  
Erdinç Dündar ◽  
Bilal Altay
Keyword(s):  
Uniform Convergence ◽  
Double Sequences ◽  
Cauchy Sequences

In this work, we discuss various kinds of I2-uniform convergence for double sequences of functions and introduce the concepts of I2 and I*2-uniform convergence, I2-uniformly Cauchy sequences for double sequences of functions. Then, we show the relation between them.

scholarly journals Lacunary Statistical Delta 2 2-Quasi Cauchy Double Sequences

2021 ◽  
Vol 09 (06) ◽  
Author(s):  
A. G. K. Ali ◽  
Keyword(s):  
Double Sequences ◽  
Cauchy Sequences

In this paper, we have introduced the extension of recently introduced notion of summability of lacunary statistical delta 2 quasi Cauchy sequences to double sequences and established some essential results using analogy.

I_2-LOCALIZED DOUBLE SEQUENCES IN METRIC SPACES

2021 ◽  
Vol 10 (6) ◽  
pp. 2877-2885
Author(s):  
C. Granados ◽  
J. Bermúdez
Keyword(s):  
Metric Spaces ◽  
The Other ◽  
Double Sequences ◽  
Other Hand ◽  
Cauchy Sequences

In this article, the notions of $ I_{2} $-localized and $ I_{2}^{*} $-localized sequences in metric spaces are defined. Besides, we study some properties associated to $ I_{2} $-localized and $ I_{2} $-Cauchy sequences. On the other hand, we define the notion of uniformly $ I_{2} $-localized sequences in metric spaces.

scholarly journals TRIANGULAR A−STATISTICAL RELATIVE UNIFORM CONVERGENCE FOR DOUBLE SEQUENCES OF POSITIVE LINEAR OPERATORS

2021 ◽  
pp. 065
Author(s):  
Selin Çınar
Keyword(s):  
Uniform Convergence ◽  
Approximation Theorem ◽  
Dimensional Space ◽  
Linear Operators ◽  
Two Dimensional ◽  
Double Sequences ◽  
The Real ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Relative Uniform Convergence

In this paper, we introduce the concept of triangular A-statistical relative convergence for double sequences of functions defined on a compactsubset of the real two-dimensional space. Based upon this new convergencemethod, we prove Korovkin-type approximation theorem. Finally, we give some further developments.

scholarly journals I_2-Relative uniform convergence and Korovkin type approximation

2021 ◽  
Vol 25 (2) ◽  
pp. 189-200
Author(s):  
Sevda Yildiz
Keyword(s):  
Uniform Convergence ◽  
Approximation Theorem ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Relative Uniform Convergence ◽  
New Type ◽  
First Time

In the present paper, an interesting type of convergence named ideal relative uniform convergence for double sequences of functions has been introduced for the first time. Then, the Korovkin type approximation theorem via this new type of convergence has been proved. An example to show that the new type of convergence is stronger than the convergence considered before has been given. Finally, the rate of  I2-relative uniform convergence has been computed.

scholarly journals Statistical Order Convergence and Statistically Relatively Uniform Convergence in Riesz Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Xuemei Xue ◽  
Jian Tao
Keyword(s):  
Uniform Convergence ◽  
Statistical Convergence ◽  
Banach Lattices ◽  
Order Convergence ◽  
Riesz Spaces ◽  
Monotone Sequences ◽  
Cauchy Sequences ◽  
Relatively Uniform Convergence

A new concept of statistically e-uniform Cauchy sequences is introduced to study statistical order convergence, statistically relatively uniform convergence, and norm statistical convergence in Riesz spaces. We prove that, for statistically e-uniform Cauchy sequences, these three kinds of convergence for sequences coincide. Moreover, we show that the statistical order convergence and the statistically relatively uniform convergence need not be equivalent. Finally, we prove that, for monotone sequences in Banach lattices, the norm statistical convergence coincides with the weak statistical convergence.

scholarly journals The λ ̅-statistically convergent double sequences in fuzzy normed spaces

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 153-163
Author(s):  
Omer Kisi
Keyword(s):  
Double Sequences ◽  
Normed Spaces ◽  
Cauchy Sequences ◽  
Convergent Sequences

We introduce double ? ?-statistically convergent sequences and double ? ?- statistically Cauchy sequences in the fuzzy normed spaces. We study [V,? ?] and [C,1]-summabilities for double sequences. In addition, we obtain the relation between these concepts and ? ?-statistically convergence.

scholarly journals On the Topological and Uniform Structure of Diversities

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Andrew Poelstra
Keyword(s):  
Uniform Convergence ◽  
Natural Transformation ◽  
Uniform Continuity ◽  
Uniform Structure ◽  
Natural Analogue ◽  
Uniform Spaces ◽  
Tight Span ◽  
Cauchy Sequences ◽  
Analytical Properties ◽  
Uniformly Continuous

Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note, we consider the analytical properties of diversities, in particular the generalizations of uniform continuity, uniform convergence, Cauchy sequences, and completeness to diversities. We develop conformities, a diversity analogue of uniform spaces, which abstract these concepts in the metric case. We show that much of the theory of uniform spaces admits a natural analogue in this new structure; for example, conformities can be defined either axiomatically or in terms of uniformly continuous pseudodiversities. Just as diversities can be restricted to metrics, conformities can be restricted to uniformities. We find that these two notions of restriction, which are functors in the appropriate categories, are related by a natural transformation.

$\bar \lambda $-statistically convergent double sequences in probabilistic normed spaces

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
E. Savaş ◽  
S. Mohiuddine
Keyword(s):  
Normed Space ◽  
Double Sequences ◽  
Normed Spaces ◽  
Probabilistic Normed Space ◽  
Probabilistic Normed Spaces ◽  
Cauchy Sequences

AbstractThe purpose of this paper is to introduce and study the concepts of double $\bar \lambda $-statistically convergent and double $\bar \lambda $-statistically Cauchy sequences in probabilistic normed space.

scholarly journals On (λ,μ)- Zweier ideal convergence in intuitionistic fuzzy normed space

2020 ◽  
Vol 30 (4) ◽  
pp. 413-427
Author(s):  
Vakeel Khan ◽  
Mobeen Ahmad
Keyword(s):  
Normed Space ◽  
Double Sequences ◽  
Real Numbers ◽  
Fuzzy Normed Space ◽  
Positive Real ◽  
Ideal Convergence ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Cauchy Sequences ◽  
New Type

In this paper, we study and introduce a new type of convergence, namely (?,?)- Zweier convergence and (?,?)- Zweier ideal convergence of double sequences x = (xij) in intuitionistic fuzzy normed space (IFNS), where ? = (?n) and ?= (?m) are two non-decreasing sequences of positive real numbers such that each tending to infinity. Furthermore, we studied (?,?)- Zweier Cauchy and (?,?)- Zweier ideal Cauchy sequences on the said space and established a relation between them.

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