English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we have found a necessary and sufficient condition forequivalence of two norms on a linear space using the theory of exponentialvector space. Exponential vector space is an ordered algebraic structure whichcan be considered as an algebraic ordered extension of vector space. Thisstructure is axiomatised on the basis of the intrinsic properties of thehyperspace $\mathscr{C}(\mathcal X)$ comprising all nonempty compact subsets ofa Hausdorff topological vector space $\mathcal X$. Exponential vector space isa conglomeration of a semigroup structure, a scalar multiplication and acompatible partial order. We have shown that the collection of all normsdefined on a linear space, together with the constant function zero, forms atopological exponential vector space. Then using the concept of comparingfunction (a concept defined on a topological exponential vector space) we haveproved the aforesaid necessary and sufficient condition; also we have provedusing comparing function that in an infinite dimensional linear space there areuncountably many non-equivalent norms.

Characterisation of equivalent norms on a linear space using exponential vector space