Functional Equations and Applications-4 :

Nowadays, the field of functional equations is an ever-growing branch of mathematics with far-reaching applications. It is increasingly used to investigate many problems in science and technology. 

The theory of functional equations is relatively new and it contributes to the development of strong tools in contemporary mathematics. Conversely, many mathematical ideas in different fields have become essential to the foundation of functional equations. 

Many new applied problems and theories have inspired and encouraged specialists on functional equations to develop new approaches and new methods.

             Applications of functional equations

Functional equations arise in many fields of mathematics, such as mechanics, geometry, statistics, measure theory, algebraic geometry, and group theory.

 Functional equations have many interesting applications in characterization problems of probability theory. 

Solutions of functional equations can be used in characterizing joint distributions from conditional distributions. 

Functional equations find many applications in the study of stochastic processes, classical mechanics, astronomy, economics, dynamic ,programming, game theory, computer graphics, neural networks, digital image processing, statistics, information theory, coding theory, fuzzy set theory, decision theory, artificial intelligence, cluster analysis, multivalued logic, population ethics, and many other fields.

We present some examples to illustrate how functional equations are applied to solve some interesting problems in geometry, finance, information theory, and wireless sensor networks.