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 Ideal convergent function sequences in random 2-normed spaces

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 557-567
Author(s):  
Ekrem Savaş ◽  
Mehmet Gürdal
Keyword(s):  
Uniform Convergence ◽  
Recent Work ◽  
Pointwise Convergence ◽  
Normed Spaces ◽  
Basic Properties ◽  
Convergence Of Sequences

In the present paper we are concerned with I-convergence of sequences of functions in random 2-normed spaces. Particularly, following the line of recent work of Karakaya et al. [23], we introduce the concepts of ideal uniform convergence and ideal pointwise convergence in the topology induced by random 2-normed spaces, and give some basic properties of these concepts.

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

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.

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

Around Taylor’s Theorem on the Convergence of Sequences of Functions

2021 ◽  
Vol 78 (1) ◽  
pp. 129-138
Author(s):  
Grażyna Horbaczewska ◽  
Patrycja Rychlewicz
Keyword(s):  
Uniform Convergence ◽  
Pointwise Convergence ◽  
Full Measure ◽  
Classical Theorem ◽  
Basic Properties ◽  
Measurable Set ◽  
Small Measure ◽  
Convergence Of Sequences ◽  
Sequence Of Functions

Abstract Egoroff’s classical theorem shows that from a pointwise convergence we can get a uniform convergence outside the set of an arbitrary small measure. Taylor’s theorem shows the possibility of controlling the convergence of the sequences of functions on the set of the full measure. Namely, for every sequence of real-valued measurable factions |fn } n∈ℕ pointwise converging to a function f on a measurable set E, there exist a decreasing sequence |δn } n∈ℕ of positive reals converging to 0 and a set A ⊆ E such that E \ A is a nullset and lim n → + ∞ | f n ( x ) − f ( x ) | δ n = 0   for   all   x ∈ A .   Let   J ( A ,   { f n } ) {\lim _{n \to + \infty }}\frac{{|{f_n}(x) - f(x)|}}{{{\delta _n}}} = 0\,{\rm{for}}\,{\rm{all}}\,x \in A.\,{\rm{Let}}\,J(A,\,\{ {f_n}\} ) denote the set of all such sequences |δn } n∈ℕ. The main results of the paper concern basic properties of sets of all such sequences for a given set A and a given sequence of functions. A relationship between pointwise convergence, uniform convergence and the Taylor’s type of convergence is considered.

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