scholarly journals Properties of a Complete Fuzzy Normed Algebra

2019 ◽  
Vol 16 (2) ◽  
pp. 0382
Author(s):  
Kider Et al.
Keyword(s):  
Normed Space ◽  
Zero Element ◽  
Complex Numbers ◽  
Normed Algebra ◽  
Fuzzy Normed Space ◽  
Basic Properties ◽  
Resolvent Set

          The aim of this paper is to translate the basic properties of the classical complete normed algebra to the complete fuzzy normed algebra at this end a proof of multiplication fuzzy continuous is given. Also a proof of every fuzzy normed algebra  without identity can be embedded into fuzzy normed algebra  with identity  and  is an ideal in  is given. Moreover the proof of the resolvent set of a non zero element in complete fuzzy normed space is equal to the set of complex numbers is given. Finally basic properties of the resolvent space of a complete fuzzy normed algebra is given.

scholarly journals Properties of a Complete Fuzzy Normed Algebra

2019 ◽  
Vol 16 (2) ◽  
pp. 0382
Author(s):  
Kider Et al.
Keyword(s):  
Normed Space ◽  
Zero Element ◽  
Complex Numbers ◽  
Normed Algebra ◽  
Fuzzy Normed Space ◽  
Basic Properties ◽  
Resolvent Set

          The aim of this paper is to translate the basic properties of the classical complete normed algebra to the complete fuzzy normed algebra at this end a proof of multiplication fuzzy continuous is given. Also a proof of every fuzzy normed algebra  without identity can be embedded into fuzzy normed algebra  with identity  and  is an ideal in  is given. Moreover the proof of the resolvent set of a non zero element in complete fuzzy normed space is equal to the set of complex numbers is given. Finally basic properties of the resolvent space of a complete fuzzy normed algebra is given.

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 Properties of Compact fuzzy Normed Space

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Jehad R. Kider ◽  
Noor A. Kadhum
Keyword(s):  
Normed Space ◽  
Fuzzy Normed Space ◽  
Basic Properties ◽  
Definition Of

In this paper we recall the definition of fuzzy norm then basic properties of fuzzy  normed space is recalled after that we introduced the definition of compact fuzzy  normed space. Then basic properties of compact fuzzy normed space is proved.

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 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.

Intuitionistic Fuzzy 2-Metric Space and Some Topological Properties

2013 ◽  
pp. 245-260
Author(s):  
Q.M. Danish Lohani
Keyword(s):  
Metric Space ◽  
Normed Space ◽  
Fuzzy Metric Space ◽  
Topological Properties ◽  
Fuzzy Normed Space ◽  
Fuzzy Metric ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Normed Space ◽  
Norm Space

The notion of intuitionistic fuzzy metric space was introduced by Park (2004) and the concept of intuitionistic fuzzy normed space by Saadati and Park (2006). Recently Mursaleen and Lohani introduced the concept of intuitionistic fuzzy 2-metric space (2009) and intuitionistic fuzzy 2-norm space. This paper studies precompactness and metrizability in this new setup of intuitionistic fuzzy 2-metric space.

scholarly journals On lp-Complex Numbers

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 877
Author(s):  
Wolf-Dieter Richter
Keyword(s):  
Symmetry Group ◽  
Complex Number ◽  
Common Property ◽  
Complex Numbers ◽  
Trigonometric Functions ◽  
Absolute Value ◽  
Basic Properties ◽  
The Common

Dispensing with the common property of distributivity and replacing classical trigonometric functions with their l p -counterparts in Euler’s trigonometric representation of complex numbers, classes of l p -complex numbers are introduced and some of their basic properties are proved. The collection of all points that leave the l p -absolute value of each l p -complex number invariant under l p -complex numbers multiplication is shown to be a group of elements that have l p -absolute value one but not the symmetry group.

On the Modular Value and Fractional Part of a Random Variable

1995 ◽  
Vol 9 (4) ◽  
pp. 551-562
Author(s):  
Stephen J. Herschkorn
Keyword(s):  
Fourier Series ◽  
Inversion Formula ◽  
Distribution Density ◽  
Probabilistic Method ◽  
Fractional Part ◽  
Renewal Theory ◽  
Random Variable ◽  
General Distribution ◽  
Complex Numbers ◽  
Basic Properties

Let X be a random variable with characteristic function ϕ. In the case where X is integer-valued and n is a positive integer, a formula (in terms of ϕ) for the probability that n divides X is presented. The derivation of this formula is quite simple and uses only the basic properties of expectation and complex numbers. The formula easily generalizes to one for the distribution of X mod n. Computational simplifications and the relation to the inversion formula are also discussed; the latter topic includes a new inversion formula when the range of X is finite.When X may take on a more general distribution, limiting considerations of the previous formulas suggest others for the distribution, density, and moments of the fractional part X — [X]. These are easily derived using basic properties of Fourier series. These formulas also yield an alternative inversion formula for ϕ when the range of X is bounded.Applications to renewal theory and random walks are suggested. A by-product of the approach is a probabilistic method for the evaluation of infinite series.

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