THE f-NORM; A GENERALIZATION OF THE NORM OF FUNCTIONAL ANALYSIS
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2015, Vol 11, Issue 7
Abstract
A generalisation, f-norm, of the concept of norm as defined in Functional Analysis is introduced. The norm of λx is |λ|times the norm of x . In the definiton of the f-norm, this requirement is relaxed, so that the f-norm of λx is times the f-|λ|norm of , where f is a function satisfying certain properties, which are presented. Examples of f-norms are given, the metric induced by an f-norm is considered and results concerning continuity of certain functions obtained. Sets that are convex with respect to an f-norm are studied. Limits with respect to the f-norm are also considered.
Authors and Affiliations
Norris Sookoo
Keywords
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- EP ID EP651610
- DOI 10.24297/jam.v11i7.1216
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