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 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. 

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 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 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

scholarly journals On Fixed Point Theorem in Fuzzy Normed Space

2015 ◽  
Vol 18 (4) ◽  
pp. 139-143
Author(s):  
Rana A. Mohammed ◽  
◽  
Buthainah A. A. Ahmed ◽  
Fadhel F. S. ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Normed Space ◽  
Fuzzy Normed Space

ON THE HYPERSTABILITY OF THE DRYGAS FUNCTIONAL EQUATION ON A RESTRICTED DOMAIN

2019 ◽  
Vol 102 (1) ◽  
pp. 126-137
Author(s):  
JEDSADA SENASUKH ◽  
SATIT SAEJUNG
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Asymptotic Behaviour ◽  
Point Theorem ◽  
Normed Space ◽  
Restricted Domain ◽  
The Fixed Point Theorem ◽  
Misleading Statement

We prove hyperstability results for the Drygas functional equation on a restricted domain (a certain subset of a normed space). Our results are more general than the ones proposed by Aiemsomboon and Sintunavarat [‘Two new generalised hyperstability results for the Drygas functional equation’, Bull. Aust. Math. Soc.95 (2017), 269–280] and our proof does not rely on the fixed point theorem of Brzdęk as was the case there. A characterisation of the Drygas functional equation in terms of its asymptotic behaviour is given. Several examples are given to illustrate our generalisations. Finally, we point out a misleading statement in the proof of the second result in the paper by Aiemsomboon and Sintunavarat and propose its correction.

scholarly journals Fixed point theorem in ultrametric space

2018 ◽  
Vol 12 (2) ◽  
pp. 336-346
Author(s):  
Hamid Mamghaderi ◽  
Hashem Masiha
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Normed Space ◽  
Fixed Point Theorems ◽  
Ultrametric Space ◽  
Weak Connectivity ◽  
The Relationship

We give a class of generalizations of a number of known fixed point theorems to mappings defined on an ultrametric space and non-Archimedean normed space which are endowed with a graph. We also investigate the relationship between weak connectivity and the existence of fixed points for these mappings.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion
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