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 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.

The Fréchet Variation, Sector Limits, and Left Decompositions

1950 ◽  
Vol 2 ◽  
pp. 344-374 ◽  
Author(s):  
Marston Morse ◽  
William Transue
Keyword(s):  
Fourier Series ◽  
Variational Analysis ◽  
Cartesian Product ◽  
Multiple Fourier Series ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Variation Of A Function ◽  
De La Vallée Poussin

1. Introduction. The Fréchet variation of a function g defined over a 2-interval I2 was introduced by Fréchet to enable him to generalize Riesz's theorem on the representation of functionals linear over the space C [7]. Recently the authors have found this variation fundamental in the study of functionals bilinear over the Cartesian product A ⨯ B of two normed linear spaces with certain characteristic properties, and in the further use of this theory in spectral and variational analysis. The recent discovery by the authors of several new properties of the Fréchet variation has made it possible to to give new and natural tests for the convergence of multiple Fourier series generalizing the classical Jordan, de la Vallée Poussin, Dini, Young and Lebesgue tests under considerably less restrictive hypotheses than those now accepted.

Intuitionistic Fuzzy Pseudo-Normed Linear Spaces

2018 ◽  
Vol 15 (01) ◽  
pp. 113-127
Author(s):  
Bivas Dinda ◽  
Santanu Kumar Ghosh ◽  
T. K. Samanta
Keyword(s):  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Intuitionistic Fuzzy ◽  
Definition Of

We introduce the definition of intuitionistic fuzzy pseudo-norm and study some properties of convergence and [Formula: see text]-convergence in intuitionistic fuzzy pseudo-normed linear spaces.

scholarly journals Multilinear Operator and Its Basic Properties

2019 ◽  
Vol 27 (1) ◽  
pp. 35-45
Author(s):  
Kazuhisa Nakasho
Keyword(s):  
Algebraic Structure ◽  
Multilinear Operator ◽  
Multilinear Operators ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Basic Properties ◽  
Normed Linear Spaces ◽  
Real Linear

Summary In the first chapter, the notion of multilinear operator on real linear spaces is discussed. The algebraic structure [2] of multilinear operators is introduced here. In the second chapter, the results of the first chapter are extended to the case of the normed spaces. This chapter shows that bounded multilinear operators on normed linear spaces constitute the algebraic structure. We referred to [3], [7], [5], [6] in this formalization.

scholarly journals On (fuzzy) pseudo-semi-normed linear spaces

2021 ◽  
Vol 7 (1) ◽  
pp. 467-477
Author(s):  
Yaoqiang Wu ◽  
Keyword(s):  
The Other ◽  
Topological Spaces ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Other Hand ◽  
Fuzzy Topological Spaces

<abstract><p>In this paper, we introduce the notion of pseudo-semi-normed linear spaces, following the concept of pseudo-norm which was presented by Schaefer and Wolff, and illustrate their relationship. On the other hand, we introduce the concept of fuzzy pseudo-semi-norm, which is weaker than the notion of fuzzy pseudo-norm initiated by N$ \tilde{\rm{a}} $d$ \tilde{\rm{a}} $ban. Moreover, we give some examples which are according to the commonly used $ t $-norms. Finally, we establish norm structures of fuzzy pseudo-semi-normed spaces and provide (fuzzy) topological spaces induced by (fuzzy) pseudo-semi-norms, and prove that the (fuzzy) topological spaces are (fuzzy) Hausdorff.</p></abstract>

scholarly journals The Ck Space

2013 ◽  
Vol 21 (1) ◽  
pp. 25-31
Author(s):  
Katuhiko Kanazashi ◽  
Hiroyuki Okazaki ◽  
Yasunari Shidama
Keyword(s):  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Definition Of

Summary In this article, we formalize continuous differentiability of realvalued functions on n-dimensional real normed linear spaces. Next, we give a definition of the Ck space according to [23].

scholarly journals Continuity of Multilinear Operator on Normed Linear Spaces

2019 ◽  
Vol 27 (1) ◽  
pp. 61-65
Author(s):  
Kazuhisa Nakasho ◽  
Yasunari Shidama
Keyword(s):  
Banach Space ◽  
Linear Space ◽  
Multilinear Operator ◽  
Multilinear Operators ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Normed Linear Spaces

Summary In this article, various definitions of contuity of multilinear operators on normed linear spaces are discussed in the Mizar formalism [4], [1] and [2]. In the first chapter, several basic theorems are prepared to handle the norm of the multilinear operator, and then it is formalized that the linear space of bounded multilinear operators is a complete Banach space. In the last chapter, the continuity of the multilinear operator on finite normed spaces is addressed. Especially, it is formalized that the continuity at the origin can be extended to the continuity at every point in its whole domain. We referred to [5], [11], [8], [9] in this formalization.

A cohomological index of Fuller type for parameterized set-valued maps in normed spaces

2014 ◽  
Vol 12 (8) ◽  
Author(s):  
Robert Skiba
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Differential Inclusions ◽  
Stationary Points ◽  
Normed Spaces ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Topological Invariance ◽  
Cohomological Index

AbstractWe construct a cohomological index of the Fuller type for set-valued flows in normed linear spaces satisfying the properties of existence, excision, additivity, homotopy and topological invariance. In particular, the constructed index detects periodic orbits and stationary points of set-valued dynamical systems, i.e., those generated by differential inclusions. The basic methods to calculate the index are also presented.

scholarly journals Fixed Point Theory in Fuzzy Normed Linear Spaces: A General View

2021 ◽  
Vol 16 (6) ◽  
Author(s):  
Simona Dzitac ◽  
Horea Oros ◽  
Dan Deac ◽  
Sorin Nădăban
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Special Section ◽  
Point Theory ◽  
General View ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Definition Of ◽  
Fuzzy Fixed Point

In this paper we have presented, firstly, an evolution of the concept of fuzzy normed linear spaces, different definitions, approaches as well as generalizations. A special section is dedicated to fuzzy Banach spaces. In the case of fuzzy normed linear spaces, researchers have been working, until now, with a definition of completeness inspired by M. Grabiec’s work in the context of fuzzy metric spaces. We propose another definition and we prove that it is much more adequate, inspired by the work of A.George and P. Veeramani. Finally, some important results in fuzzy fixed point theory were highlighted.

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