Aczel J., Dhombres J. Functional equations in several variables

Digitally printed version, 2008. — Cambridge: Cambridge University Press, 1989. — 462 p. — ISBN: 978-0-521-35276-5; 978-0-521-06389-0Axiomatic motivation of vector addition
Cauchy's equation. Hamel basis
Three further Cauchy equations. An application to information theory
Generalizations of Cauchy's equations to several multiplace vector and matrix functions. An application to geometric objects
Cauchy's equations for complex functions. Applications to harmonic analysis and to information measures
Conditional Cauchy equations. An application to geometry and a characterization of the Heaviside functions
Addundancy, extensions, quasi-extensions and extensions almost everywhere. Applications to harmonic analysis and to rational decision making
D'AIembert's functional equation. An application to noneuclidean mechanics
Images of sets and functional equations. Applications to relativity theory and to additive functions bounded on particular sets
Some applications of functional equations in functional analysis, in the geometry of Banach spaces and in valuation theory
Characterizations of inner product spaces. An application to gas dynamics
Some related equations and systems of equations. Applications to combinatorics and Markov processes
Equations for trigonometric and similar functions
A class of equations generalizing d'AIembert and Cauchy Pexider-type equations
A further generalization of Pexider's equation. A uniqueness theorem.
More about conditional Cauchy equations. Applications to additive number theoretical functions and to coding theory
Mean values, mediality and self-distributivity
Generalized mediality. Connection to webs and nomograms
Further composite equations. An application to averaging theory
Homogeneity and some generalizations. Applications to economics
Historical notes