normed vector space

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normed vector space

[′nȯrmd ′vek·tər ′spās]
(mathematics)
References in periodicals archive ?
This graduate text introduces normed spaces as a way to generalize the concept of the absolute value in the setting of the real numbers, and the mathematical basis of Banach spaces and linear operators.
By the Mazur-Ulam theorem every surjective isometry between two real normed spaces is affine.
Vignoli, On the solvability of nonlinear operator equations in normed spaces, Ann.
During the last decades several stability problems of functional equations have been investigated by a number of mathematicians in various spaces, such as fuzzy normed spaces, non-Archimedean normed spaces and random normed spaces; see [4,8,9,14,3,21,30] and reference therein.
Zaslavski, Optimization on Metric and Normed Spaces, Springer, New York, 2010.
He offers an accessible account of elementary real analysis from normed spaces to Hilbert and Banach spaces, with some extended treatment of distribution theory, Fourier and Laplace analyses, and Hardy spaces, accompanied by some applications to linear systems and control theory.
To show that a normed space is a Hilbert space, we prove that the normed spaces comes from an inner product.
In (17), (18) and (20) the stability of Cauchy, quadratic and quartic functional equations in non-Archimedean normed spaces were investigated.
She covers normed spaces and operators, Frechet spaces and Banach theorems, duality, weak topologies, distributions, the Fourier transform and Sobolev spaces, Banach algebras, and unbounded operators in a Hilbert space.
2] Fatemeh Lael and Kourosh Nouruzi, compact operators defined on 2-normed and 2-Probablistic normed spaces, Mathematical Problems in Engineering Volume 2009 (2009), Article ID 950234,
com/research/d52215/difference_equatio) has announced the addition of Elsevier Science and Technology's new report "Difference Equations in Normed Spaces.