scholarly journals TEOREMA TITIK TETAP PADA RUANG NORM-n STANDAR

2012 ◽  
Vol 4 (1) ◽  
pp. 69
Author(s):  
Shelvi Ekariani ◽  
Hendra Gunawan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Normed Space ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Usual Norm

On the standard n-normed space,i.e an inner product space equipped with the standard n-norm, one can derive a norm from the n-norm in a certain way. The purpose of this note is to establish the equivalence between such a norm and the usual norm on standard n-normed space. Further, this fact together with others use to prove  a fixed point theorem on the standard n-normed space. 

The space of p-summable sequences and its natural n-norm

2001 ◽  
Vol 64 (1) ◽  
pp. 137-147 ◽  
Author(s):  
Hendra Gunawan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Normed Space ◽  
Usual Norm

We study the space lp, 1 ≤ p ≤ ∞, and its natural n-norm, which can viewed as a generalisation of its usual norm. Using a derived norm equivalent to its usual norm, we show that lp is complete with respect to its natural n-norm. In addition, we also prove a fixed point theorem for lp as an n-normed space.

scholarly journals Hyperstability of the Fréchet Equation and a Characterization of Inner Product Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Anna Bahyrycz ◽  
Janusz Brzdęk ◽  
Magdalena Piszczek ◽  
Justyna Sikorska
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Main Tool ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Fréchet Equation ◽  
New Inequalities

We prove some stability and hyperstability results for the well-known Fréchet equation stemming from one of the characterizations of the inner product spaces. As the main tool, we use a fixed point theorem for the function spaces. We finish the paper with some new inequalities characterizing the inner product spaces.

scholarly journals Onn-normed spaces

2001 ◽  
Vol 27 (10) ◽  
pp. 631-639 ◽  
Author(s):  
Hendra Gunawan ◽  
M. Mashadi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Normed Space ◽  
Normed Spaces

Given ann-normed space withn≥2, we offer a simple way to derive an(n−1)-norm from then-norm and realize that anyn-normed space is an(n−1)-normed space. We also show that, in certain cases, the(n−1)-norm can be derived from then-norm in such a way that the convergence and completeness in then-norm is equivalent to those in the derived(n−1)-norm. Using this fact, we prove a fixed point theorem for somen-Banach spaces.

scholarly journals Orthogonality in normed spaces

1986 ◽  
Vol 33 (3) ◽  
pp. 449-455 ◽  
Author(s):  
J. R. Partington
Keyword(s):  
Euclidean Space ◽  
Normed Space ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Normed Spaces ◽  
Separable Space ◽  
Orthogonality In Normed Spaces

Some properties which different definitions or orthogonality in a normed space can possess are considered. It is shown that orthogonality can be defined on any separable space with many of the properties possessed by the usual orthogonality in an inner-product space, but that the possession of a further property forces the space to be isomorphic to a Euclidean space.

scholarly journals On Carlsson type orthogonality and characterization of inner product spaces

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 859-870 ◽  
Author(s):  
Eder Kikianty ◽  
Sever Dragomir
Keyword(s):  
Normed Space ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Isosceles Orthogonality ◽  
Inner Product Spaces ◽  
Pythagorean Orthogonality

In an inner product space, two vectors are orthogonal if their inner product is zero. In a normed space, numerous notions of orthogonality have been introduced via equivalent propositions to the usual orthogonality, e.g. orthogonal vectors satisfy the Pythagorean law. In 2010, Kikianty and Dragomir [9] introduced the p-HH-norms (1 ? p < ?) on the Cartesian square of a normed space. Some notions of orthogonality have been introduced by utilizing the 2-HH-norm [10]. These notions of orthogonality are closely related to the classical Pythagorean orthogonality and Isosceles orthogonality. In this paper, a Carlsson type orthogonality in terms of the 2-HH-norm is considered, which generalizes the previous definitions. The main properties of this orthogonality are studied and some useful consequences are obtained. These consequences include characterizations of inner product space.

scholarly journals A Revisit to n-Normed Spaces Through Its Quotient Spaces

2020 ◽  
Vol 53 (2) ◽  
pp. 181-191
Author(s):  
H. Batkunde ◽  
H. Gunawan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Normed Space ◽  
Continuous Mapping ◽  
Normed Spaces ◽  
Quotient Spaces ◽  
Contractive Mappings ◽  
Bounded Set ◽  
Summable Sequence

In this paper, we define several types of continuous mapping in $n$-normed spaces with respect to the norms of its quotient spaces. Then, we show that all types of the continuity are equivalent. We also study contractive mappings on $n$-normed spaces using these norms. In particular, we prove a fixed point theorem for contractive mappings on a closed and bounded set in the $n$-normed space with respect to the norms of its quotient spaces.In the last section we prove a fixed point theorem and give some remarks on the $p$-summable sequence space as an $n$-normed space.

scholarly journals Stability of a generalization of the Fréchet functional equation

2015 ◽  
Vol 14 (1) ◽  
pp. 69-79 ◽  
Author(s):  
Renata Malejki
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Main Tool ◽  
Function Spaces ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
New Inequalities

AbstractWe prove some stability and hyperstability results for a generalization of the well known Fréchet functional equation, stemming from one of the characterizations of the inner product spaces. As the main tool we use a fixed point theorem for some function spaces. We end the paper with some new inequalities characterizing the inner product spaces.

scholarly journals SISTEM ORTONORMAL DALAM RUANG HILBERT

2014 ◽  
Vol 8 (2) ◽  
pp. 19-26
Author(s):  
Zeth A. Leleury
Keyword(s):  
Hilbert Space ◽  
Quadratic Form ◽  
Vector Space ◽  
Integral Equations ◽  
Normed Space ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Finite Dimensional

Hilbert space is one of the important inventions in mathematics. Historically, the theory of Hilbert space originated from David Hilbert’s work on quadratic form in infinitely many variables with their applications to integral equations. This paper contains some definitions such as vector space, normed space and inner product space (also called pre-Hilbert space), and which is important to construct the Hilbert space. The fundamental ideas and results are discussed with special attention given to finite dimensional pre-Hilbert space and some basic propositions of orthonormal systems in Hilbert space. This research found that each finite dimensional pre- Hilbert space is a Hilbert space. We have provided that a finite orthonormal systems in a Hilbert space X is complete if and only if this orthonormal systems is a basis of X.

scholarly journals A Study of Caristi’s Fixed Point Theorem on Normed Space and Its Applications

2021 ◽  
Vol 11 (03) ◽  
pp. 169-179
Author(s):  
Md. Abdul Mannan ◽  
Moqbul Hossain ◽  
Halima Akter ◽  
Samiran Mondal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Normed Space ◽  
Caristi’S Fixed Point Theorem ◽  
Caristi's Fixed Point Theorem
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