scholarly journals Statistical Convergence and Ideal Convergence of Sequences of Functions in 2-Normed Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Saeed Sarabadan ◽  
Sorayya Talebi
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Convergence Of Sequences

We present various kinds of statistical convergence andℐ-convergence for sequences of functions with values in 2-normed spaces and obtain a criterion forℐ-convergence of sequences of functions in 2-normed spaces. We also define the notion ofℐ-equistatistically convergence and studyℐ-equi-statistically convergence of sequences of functions.

Ideal convergence of sequences in neutrosophic normed spaces

2021 ◽  
pp. 1-10
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Convergence Of Sequences ◽  
The Ideal

Statistical convergence of sequences has been studied in neutrosophic normed spaces (NNS) by Kirişci and Şimşek [39]. Ideal convergence is more general than statistical convergence for sequences. This has motivated us to study the ideal convergence in NNS. In this paper, we study the concept of ideal convergence and ideal Cauchy for sequences in NNS.

scholarly journals λ-Statistical Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Vatan Karakaya ◽  
Necip Şimşek ◽  
Müzeyyen Ertürk ◽  
Faik Gürsoy
Keyword(s):  
Uniform Convergence ◽  
Pointwise Convergence ◽  
Statistical Convergence ◽  
Normed Spaces ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Convergence Of Sequences ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Convergent Sequences

We studyλ-statistically convergent sequences of functions in intuitionistic fuzzy normed spaces. We define concept ofλ-statistical pointwise convergence andλ-statistical uniform convergence in intuitionistic fuzzy normed spaces and we give some basic properties of these concepts.

scholarly journals On Ideal Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

2014 ◽  
Vol 8 (5) ◽  
pp. 2307-2313
Author(s):  
Vatan KARAKAYA ◽  
Necip ŞİMŞEK ◽  
M�zeyyen ERTÜRK ◽  
Faik GÜRSOY
Keyword(s):  
Normed Spaces ◽  
Ideal Convergence ◽  
Intuitionistic Fuzzy ◽  
Convergence Of Sequences ◽  
Intuitionistic Fuzzy Normed Spaces

scholarly journals Deferred statistical convergence of sequences in intuitionistic fuzzy normed spaces

2018 ◽  
Vol 24 (3) ◽  
pp. 64-78
Author(s):  
S. Melliani ◽  
◽  
M. Küçükaslan ◽  
H. Sadiki ◽  
L. S. Chadli ◽  
...  
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Intuitionistic Fuzzy ◽  
Convergence Of Sequences ◽  
Intuitionistic Fuzzy Normed Spaces

On I-convergence in random 2-normed spaces

2011 ◽  
Vol 61 (6) ◽  
Author(s):  
M. Mursaleen ◽  
Abdullah Alotaibi
Keyword(s):  
Banach Spaces ◽  
Normed Space ◽  
Statistical Convergence ◽  
Normed Spaces ◽  
Ideal Convergence

AbstractRecently the concepts of statistical convergence and ideal convergence have been studied in 2-normed and 2-Banach spaces by various authors. In this paper we define and study the notion of ideal convergence in random 2-normed space and construct some interesting examples.

On ideal convergence in probabilistic normed spaces

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
M. Mursaleen ◽  
S. Mohiuddine
Keyword(s):  
Normed Space ◽  
Statistical Convergence ◽  
Normed Spaces ◽  
Probabilistic Normed Space ◽  
Ideal Convergence ◽  
Probabilistic Normed Spaces ◽  
Real Anal ◽  
The Relationship ◽  
Cluster Points ◽  
Interesting Generalization

AbstractAn interesting generalization of statistical convergence is I-convergence which was introduced by P.Kostyrko et al [KOSTYRKO,P.—ŠALÁT,T.—WILCZYŃSKI,W.: I-Convergence, Real Anal. Exchange 26 (2000–2001), 669–686]. In this paper, we define and study the concept of I-convergence, I*-convergence, I-limit points and I-cluster points in probabilistic normed space. We discuss the relationship between I-convergence and I*-convergence, i.e. we show that I*-convergence implies the I-convergence in probabilistic normed space. Furthermore, we have also demonstrated through an example that, in general, I-convergence does not imply I*-convergence in probabilistic normed space.

The Arzelà–Ascoli theorem by means of ideal convergence

2018 ◽  
Vol 25 (3) ◽  
pp. 475-479
Author(s):  
Emre Taş ◽  
Tugba Yurdakadim
Keyword(s):  
Uniform Convergence ◽  
Pointwise Convergence ◽  
Statistical Convergence ◽  
Real Numbers ◽  
Ideal Convergence ◽  
Convergence Of Sequences ◽  
The Relationship

AbstractIn this paper, using the concept of ideal convergence, which extends the idea of ordinary convergence and statistical convergence, we are concerned with the I-uniform convergence and the I-pointwise convergence of sequences of functions defined on a set of real numbers D. We present the Arzelà–Ascoli theorem by means of ideal convergence and also the relationship between I-equicontinuity and I-continuity for a family of functions.

scholarly journals On generalized difference ideal convergence in random 2-normed spaces

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1273-1282 ◽  
Author(s):  
Bipan Hazarika
Keyword(s):  
Real Number ◽  
Normed Spaces ◽  
Real Numbers ◽  
Ideal Convergence ◽  
Cauchy Sequences ◽  
Convergence Of Sequences ◽  
Positive Integers

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In [17], Kostyrko et. al introduced the concept of ideal convergence as a sequence (xk ) of real numbers is said to be I-convergent to a real number ?, if for each ? > 0 the set {k ? N : |xk ? ?| ? ?} belongs to I. In [28], Mursaleen and Alotaibi introduced the concept of I-convergence of sequences in random 2-normed spaces. In this paper, we define and study the notion of ?n -ideal convergence and ?n -ideal Cauchy sequences in random 2-normed spaces, and prove some interesting theorems.

scholarly journals Statistical Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Vatan Karakaya ◽  
Necip Şimşek ◽  
Müzeyyen Ertürk ◽  
Faik Gürsoy
Keyword(s):  
Statistical Convergence ◽  
Normed Spaces ◽  
Intuitionistic Fuzzy ◽  
Convergence Of Sequences ◽  
Intuitionistic Fuzzy Normed Spaces

The purpose of this work is to investigate types of convergence of sequences of functions in intuitionistic fuzzy normed spaces and some properties related with these concepts.

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