New generalization of norm spaces and applications

Document Type : Research Paper


1 Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran

2 Department of Pure Mathematics, University of Sharekord, Sharekord, Iran


One of the generalizations that were studied from metric space was multiplicative metric space. The main idea was that the usual triangular inequality was replaced by a  multiplicative triangle inequality. The important thing is that logarithm of every multiplicative metric is a  metric. In this paper, we introduce multiplicative norm space and present three norms in bounded multiplicative operator spaces and we investigate conditions that bounded multiplicative operator spaces be complete norm multiplicative spaces. It is notable that the logarithm of every multiplicative norm is not a norm and so we have new results in multiplicative norm spaces. We give an important extension of the Hahn-Banach theorem to nonlinear operators and their ramifications and indicate some applications.


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Volume 14, Issue 10
October 2023
Pages 303-314
  • Receive Date: 17 June 2021
  • Revise Date: 11 February 2022
  • Accept Date: 13 March 2022