The book provides a comprehensive overview of the characterizations
of real normed spaces as inner product spaces based on norm
derivatives and generalizations of the most basic geometrical
properties of triangles in normed spaces. Since the appearance of
Jordan-von Neumann's classical theorem (The Parallelogram Law) in
1935, the field of characterizations of inner product spaces has
received a significant amount of attention in various literature
texts. Moreover, the techniques arising in the theory of functional
equations have shown to be extremely useful in solving key problems
in the characterizations of Banach spaces as Hilbert spaces.This
book presents, in a clear and detailed style, state-of-the-art
methods of characterizing inner product spaces by means of norm
derivatives. It brings together results that have been scattered in
various publications over the last two decades and includes more
new material and techniques for solving functional equations in
normed spaces. Thus the book can serve as an advanced undergraduate
or graduate text as well as a resource book for researchers working
in geometry of Banach (Hilbert) spaces or in the theory of
functional equations (and their applications).
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