scholarly journals New Fuzzy Normed Spaces

2012 ◽  
Vol 9 (3) ◽  
pp. 559-564 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Continuous Convergence ◽  
Definition Of

In this paper the research introduces a new definition of a fuzzy normed space then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.

scholarly journals Ideal Convergence and Completeness of a Normed Space

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 897 ◽  
Author(s):  
Fernando León-Saavedra ◽  
Francisco Javier Pérez-Fernández ◽  
María del Pilar Romero de la Rosa ◽  
Antonio Sala
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Convergence Space ◽  
Normed Spaces ◽  
Ideal Convergence ◽  
Underlying Space ◽  
Phd Thesis

We aim to unify several results which characterize when a series is weakly unconditionally Cauchy (wuc) in terms of the completeness of a convergence space associated to the wuc series. If, additionally, the space is completed for each wuc series, then the underlying space is complete. In the process the existing proofs are simplified and some unanswered questions are solved. This research line was originated in the PhD thesis of the second author. Since then, it has been possible to characterize the completeness of a normed spaces through different convergence subspaces (which are be defined using different kinds of convergence) associated to an unconditionally Cauchy sequence.

scholarly journals Strongly Lacunary Ward Continuity in 2-Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hüseyin Çakalli ◽  
Sibel Ersan
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Normed Spaces ◽  
Cauchy Sequences

A functionfdefined on a subsetEof a 2-normed spaceXis strongly lacunary ward continuous if it preserves strongly lacunary quasi-Cauchy sequences of points inE; that is,(f(xk))is a strongly lacunary quasi-Cauchy sequence whenever (xk) is strongly lacunary quasi-Cauchy. In this paper, not only strongly lacunary ward continuity, but also some other kinds of continuities are investigated in 2-normed spaces.

scholarly journals Some fixed point theorems in n-normed spaces

2020 ◽  
Vol 25 (3) ◽  
pp. 1-15 ◽  
Author(s):  
Hanan Sabah Lazam ◽  
Salwa Salman Abed
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Normed Space ◽  
Fixed Point Theorems ◽  
Normed Spaces ◽  
Weak Contraction ◽  
Contraction Mappings ◽  
Basic Properties ◽  
Definition Of

In this article, we recall the definition of a real n-normed space and some basic properties. fixed point theorems for types of Kannan, Chatterge, Zamfirescu, -Weak contraction and  - (,)-Weak contraction mappings in  Banach spaces.

scholarly journals Ideally Statistical Convergence in n-normed Space

2020 ◽  
pp. 75-84
Author(s):  
Nazneen Khan ◽  
Amani Shatarah
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Topological Properties ◽  
Normed Spaces

The aim of the article is to extend the concept of Ideally statistical convergence from 2 normed spaces to n-normed space. We have also study and prove some important algebraic and topological properties of Ideally-statistical convergence of real sequences in n-normed space. In the last part of this article we obtain a criterion for I-statistically Cauchy sequence in n-normed space to be I-statistically Cauchy with respect to ∥.∥∞.

scholarly journals Some Results on G-Normed Linear Spaces

2020 ◽  
Vol 55 (3) ◽  
Author(s):  
Maiada Nazar Mohammedali ◽  
Raghad Ibraham Sabri ◽  
Mohammed Rasheed ◽  
Suha Shihab
Keyword(s):  
Normed Space ◽  
Cartesian Product ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Definition Of

In the present work, our goal is to define the Cartesian product of two generalized normed spaces depending on the notion of generalized normed space. It is a background to state and prove that the Cartesian product of two complete generalized normed spaces is also a complete generalized normed space. Furthermore, the definition of the pseudo-generalized normed space is introduced and essential concepts related to this space are discussed and proved.

scholarly journals Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces

2019 ◽  
Vol 16 (1) ◽  
pp. 0104
Author(s):  
Kider Et al.
Keyword(s):  
Compact Operator ◽  
Normed Space ◽  
Bounded Operator ◽  
Convergent Subsequence ◽  
Compact Operators ◽  
Bounded Sequence ◽  
Linear Operators ◽  
Fuzzy Normed Space ◽  
Basic Properties ◽  
Definition Of

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact operators. Finally, if T belongs to FC(V,U) and dimension of V is finite then T is fuzzy compact is proved.

scholarly journals n-Tuplet Coincidence Point Theorems in Intuitionistic Fuzzy Normed Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Müzeyyen Ertürk ◽  
Vatan Karakaya
Keyword(s):  
Fixed Point ◽  
Normed Space ◽  
Coincidence Point ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Coincidence Points ◽  
Tripled Fixed Point ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Intuitionistic Fuzzy Normed Spaces

For an arbitrarynpositive integer, we investigate the existence ofn-tuplet coincidence points in intuitionistic fuzzy normed space. Results of the paper are more general than those of the coupled and the tripled fixed point works in intuitionistic fuzzy normed space.

scholarly journals Nonlinear L-fuzzy stability of k-cubic functional equation

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1137-1148 ◽  
Author(s):  
Reza Saadati ◽  
Yeol Cho ◽  
John Rassias
Keyword(s):  
Functional Equation ◽  
Set Theory ◽  
Normed Space ◽  
Lattice Theory ◽  
Functional Equations ◽  
Stability Result ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Cubic Functional Equation ◽  
The Stability

In this paper, we establish the stability result for the k-cubic functional equation 2[kf (x+ky)+f (kx-y)]=k(k2+1)[f(x+y)+f(x-y)] + 2(k4-1) f(y), where k is a real number different from 0 and 1, in the setting of various L-fuzzy normed spaces that in turn generalize a Hyers-Ulam stability result in the framework of classical normed spaces. First we shall prove the stability of k-cubic functional equations in the L-fuzzy normed space under arbitrary t-norm which generalizes previous works. Then we prove the stability of k-cubic functional equations in the non- Archimedean L-fuzzy normed space. We therefore provide a link among different disciplines: fuzzy set theory, lattice theory, non-Archimedean spaces and mathematical analysis.

scholarly journals Schauder Basis, Separability, and Approximation Property in Intuitionistic Fuzzy Normed Space

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
M. Mursaleen ◽  
V. Karakaya ◽  
S. A. Mohiuddine
Keyword(s):  
Normed Space ◽  
Approximation Property ◽  
Sequence Spaces ◽  
Schauder Basis ◽  
Normed Spaces ◽  
Fuzzy Normed Space ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Intuitionistic Fuzzy Normed Spaces

We define and study the concepts of Schauder basis, separability, and approximation property in intuitionistic fuzzy normed spaces and establish some results related to these concepts. We also display here some interesting examples by using classical sequence spaces .

scholarly journals ON $\mathcal{I}_2$-CONVERGENCE AND $\mathcal{I}_2$-CAUCHY DOUBLE SEQUENCES OF FUNCTIONS IN 2-NORMED SPACES

2020 ◽  
pp. 801
Author(s):  
Sevim Yegül ◽  
Erdinç Dündar
Keyword(s):  
Normed Space ◽  
Cauchy Sequence ◽  
Double Sequences ◽  
Normed Spaces

In this study, firstly, we studied some properties of $\mathcal{I}_2$-convergence. Then, we introduced $\mathcal{I}_2$-Cauchy and $\mathcal{I}_2^*$-Cauchy sequence of double sequences of functions in $2$-normed space. Also, were investigated relationships between them for double sequences of functions in $2$-normed spaces.

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