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.
Subject
Marketing,Organizational Behavior and Human Resource Management,Strategy and Management,Drug Discovery,Pharmaceutical Science,Pharmacology
Cited by
2 articles.
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1. F-normed spaces and linear operators;Journal of Interdisciplinary Mathematics;2021-05-19
2. Convexity and continuous linear operators with respect to thef-norm;Journal of Interdisciplinary Mathematics;2019-01-02