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
Vignoli, On the solvability of nonlinear operator equations in normed spaces
Statistical convergence of double sequences in fuzzy normed spaces
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
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