Theory of Approximate Functional Equations: In Banach Algebras, Inner Product Spaces and Amenable Groups

Presently no other book deals with the stability problem of functional equations in Banach algebras, inner product spaces and amenable groups. Moreover, in most stability theorems for functional equations, the completeness of the target space of the unknown functions contained in the equation is assumed. Recently, the question, whether the stability of a functional equation implies this completeness, has been investigated by several authors.

In this book the authors investigate these developments in the theory of approximate functional equations.

A useful text for graduate seminars and of interest to a wide audience including mathematicians and applied researchersPresents recent developments in the theory of approximate functional equationsDiscusses the stability problem of functional equations in Banach algebras, inner product spaces and amenable groups

1. Introduction
2. Approximate Cauchy functional equations and completeness
3. Stability of mixed type functional equations
4. Stability of functional equations in Banach algebras
5. Stability of functional equations in inner product spaces
6. Amenability of groups (semigroups) and the stability of functional equations