fnorm

Fnorm is a conventional notation used in mathematics to denote a norm associated with a function or a function space. It is not a single fixed quantity; its exact form depends on the context and the function space under consideration. In many texts, fnorm appears as shorthand for the size or length of a function.

Common examples include:

- Lp norms on a measure space (X, μ): ||f||_p = (∫_X |f(x)|^p dμ)^{1/p} for 1 ≤ p < ∞, and ||f||∞ = ess sup_{x∈X} |f(x)|. These quantify the magnitude of f in different ways as p varies.

- Sobolev norms on a domain Ω ⊂ R^n: ||f||_{W^{k,p}(Ω)} = [ Σ_{|α|≤k} ∥D^α f∥_{L^p(Ω)}^p ]^{1/p}, measuring both size and smoothness of f.

- Other function-space norms such as Hölder, BV, and Besov norms, which quantify continuity, variation, or smoothness properties of functions.

- F-norms: in fuzzy analysis, an F-norm generalizes the idea of a norm to a fuzzy normed space, defined via a function N(x, t) that measures the degree of smallness of x at scale t, satisfying a set of axioms.

In computational contexts, fnorm may appear as a function name to compute a size measure (for example, a Frobenius norm) of a matrix or an array, though exact naming varies by software library.

See also: norm; Lp norm; Sobolev norm; Frobenius norm; fuzzy norm.