A study on completely equivalent generalized normed spaces

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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

 

  1. Department of Mathematics, Vasantrao Naik Mahavidyalaya, Cidco, Aurangabad, Maharshtra, India.

2,5. Department of Mathematics, Abyan University, Abyan 80425, Yemen.

  1. 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.