normed space

normed space

(mathematics)
A vector space with a function, ||F||, such that

||F|| = 0 if and only if F=0 ||aF|| = abs(a) * ||F|| ||F+G|| <= ||F|| + ||G||

Roughly, a distance between two elements in the space is defined.
References in periodicals archive ?
By an orthogonality normed space, we mean an orthogonality space having a normed structure.
Let (X, q) be a semi normed space over the field C of complex numbers with the semi norm q.
To show that a normed space is a Hilbert space, we prove that the normed spaces comes from an inner product.
In this paper we consider the notion of intuitionistic fuzzy normed space (briefly IFNS), and we define and deal with A-statistical convergence on IFNS, where A = [([a.
Kaiser in (14) proved the stability of monomial functional equation where the functions map a normed space over a field with valuation to a Banach space over a field with valuation and the control function is of the form [epsilon]([||x||.
The concept of a linear 2-normed space was introduced as a natural 2-metric analogue of that of a normed space.
Many problems for partial difference and integro-difference equations can be written as difference equations in a normed space.
Now we are set to generalize the concept of a normed space.
Misra, The semi normed space defined by a double gai sequence of modulus function, Fasciculi Math.
The notion of the probabilistic normed space (briefly, the PN space) was first introduced by Sertnev (1962) [1] in order to study the best approximation.
1) was first proved by Skof (19) for functions from a normed space into a Banach space.
Hensel (13) has introduced a normed space which does not have the Archimedean property.