Abstract
This chapter presents the generalization and applications of Cauchy's functional equation, d’Alembert's functional equation, and Poisson distributions. The applications of functional equations were found much earlier than any systematic theory could develop. So the functional equations important for the applications were more or less solved, while the research aiming on the development of a somewhat systematic theory has begun only in these last decades. The cartesian square of a real interval can be replaced by more general domains too that in fact again is important for applications in information theory ( for example, to the uniqueness problem of entropies of the form). There are other important applications in the theory of mean values in statics (the center of gravity) and to the functional equation of bisymmetry. The chapter provides a few characteristics of this development. There is still much to do about functional equations to build up a general, genuinely qualitative theory and also to solve quite a few special equations important for theory and applications.
Published Version
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