A study on completely equivalent generalized normed spaces ∗

Jayashree  Patil; Basel Hardan; Ahmed A Hamoud; Kirtiwant P Ghadle; Alaa A Abdalla

doi:10.48165/bpas.2023.42E.1.1

Authors

Jayashree Patil Department of Mathematics, Vasantrao Naik Mahavidyalaya, Cidco, Aurangabad, Maharshtra, India.
Basel Hardan Department of Mathematics, Abyan University, Abyan 80425, Yemen.
Ahmed A Hamoud Department of Mathematics, Taiz University, Taiz P.O. Box 6803, Yemen
Kirtiwant P Ghadle Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, Maharashtra, India.
Alaa A Abdalla Department of Mathematics, Abyan University, Abyan 80425, Yemen

DOI:

https://doi.org/10.48165/bpas.2023.42E.1.1

Keywords:

Normed space, Banach space, Equivalent

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 equiv alent on linear n-Banach spaces are obtained.

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