THE f-NORM; A GENERALIZATION OF THE NORM OF FUNCTIONAL ANALYSIS - Sookoo, Norris (JOURNAL OF ADVANCES IN MATHEMATICS, 2015)
A generalisation, f-norm, of the concept of norm as defined in Functional Analysis is introduced. The norm of Î»x is |Î»|times the norm of x . In the definiton of the f-norm, this requirement is relaxed, so that the f-norm of Î»x is times the f-|Î»|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.