A study on completely equivalent generalized normed spaces
9.38$
A study on completely equivalent generalized normed spaces
Jayashree Patil1, Basel Hardan2, Ahmed A. Hamoud3, Kirtiwant P. Ghadle4 and Alaa A. Abdallah5
BPAS-E-Math and Stat. Vol.42E(1) June 2023
DOI: 10.48165/bpas.2023.42E.1.1
Page: 1-4
Description
Description
A study on completely equivalent generalized normed spaces
Jayashree Patil1, Basel Hardan2, Ahmed A. Hamoud3, Kirtiwant P. Ghadle4 and Alaa A. Abdallah5
- Department of Mathematics, Vasantrao Naik Mahavidyalaya, Cidco, Aurangabad, Maharshtra, India.
2,5. Department of Mathematics, Abyan University, Abyan 80425, Yemen.
- Department of Mathematics, Taiz University, Taiz P.O. Box 6803, Yemen.
2, 4. Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, Maharashtra, India.
1 . E-mail: jv.patil29@gmail.com , 2. E-mail: bassil2003@gmail.com, 3.E-mail: ahmed.hamoud@taiz.edu.ye , 4. E-mail: ghadle.maths@bamu.ac.in, 5. E-mail: maths.aab@bamu.ac.in
∗ Communicated, edited and typeset in Latex by Lalit Mohan Upadhyaya (Editor-in-Chief).
Received August 28, 2022 / Revised April 17, 2023 / Accepted May 07, 2023. Online First Published
on June 30, 2023 at https://www.bpasjournals.com/.
Corresponding author Basel Hardan, E-mail: bassil2003@gmail.com
Abstract
According to intuition, two spaces $X$ and $Y$ are equivalent if they may be bent, shrunk, or expanded into one another. Spaces that are homotopy-equivalent to a point are called contractible. A vector space can be equipped with more than one norm. In this paper, the necessary and sufficient conditions for n-norms to be completely equivalent on linear $n$ -Banach spaces are obtained.
