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.
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
Probabilistic normed spaces
were first defined by Serstnev in 1962 (see (28)).
Ordered normed spaces
and cones have applications in applied mathematics (see, e.
Then C is a category; it is called the category of probabilistic normed spaces
and denoted by Pn.
It is well known that every surjective isometry between normed spaces
must be linear (31), (46).
Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces