normed linear space

normed linear space

[′nȯrmd ′lin·ē·ər ′spās]
(mathematics)
A vector space which has a norm defined on it. Also known as normed vector space.
References in periodicals archive ?
where X * denotes the dual space of real normed linear space X and (.
We begin with the definition of a non-Archimedean filed and a non-Archimedean normed linear space.
in the definition of stability whenever we are working in normed linear space or
The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space
New topics have also been added including the compactness of the unit ball as a criterion of finite dimensionality of a normed linear space, the QR algorithm for finding the eigenvalues of a self-adjoint matrix, the Householder algorithm for turning such matrices into tridiagonal form, and the analogy between the convergence of the QR algorithm and Moser's theorem on the asymptotic behavior of the Toda flow as time tends to infinity.
He covers the construction of real and complex numbers, metric and Euclidean spaces, complete metric spaces, normed linear spaces, differentiation, integration, and Fourier analysis on locally compact abelian groups.
1945), Orthogonality in Normed Linear Spaces, Duke Math.
The first seven chapters cover the usual topics of point-set or general topology, including topological spaces, new spaces from old ones, connectedness, the separation and countability axioms, and metrizability and paracompactness, as well as special topics such as contraction mapping in metric spaces, normed linear spaces, the Frechet derivative, manifolds, fractals, compactifications, the Alexander subbase, and the Tychonoff theorems.
One can easily see that these are normed linear spaces and [C.
Pehlivan, Statistical convergence in fuzzy normed linear spaces, Fuzzy Sets and Systems, 159(2008), 361-370.
Their topics reflect the preferences in their own research over the past decade: discrete inequalities, integral inequalities for convex functions, Ostrowski and trapezoid type inequalities, Gruss type inequalities and related results, inequalities in inner product spaces, and inequalities in normed linear spaces and for functionals.
Xiao starts by describing sets, relations, functions, cardinals, ordinals, reals, basic theorems and sequence limits, proceeding to Riemann integrals, Riemann-Stieltjes integrals, Lebesque-Radon-Stieltjes integrals, metric spaces, continuous maps, normed linear spaces, Banach spaces via operators and functionals, and Hilbert spaces and their operators.