On Functions and Functional Equations

Abstract

FUNCTIONS Elementary properties of functions Continuous functions Derivatives of a function FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES Introduction The Cauchy functional equation and related equations Other important types of equations Applications of functional equations in several variables Discontinuous solution of the Cauchy functional equation Concluding remarks ITERATIONS Introduction Fixed points Cycles Chaos Stability Concluding remarks APPLICATIONS OF ITERATIONS Introduction A discrete model of population growth for a single biological species A discrete model of epidemics A discrete population growth model for two species FUNCTIONAL EQUATIONS IN ONE VARIABLE Introduction Characteristic mappings and invariants Linear functional equations The Abel and Schroder equations Concluding remarks REFERENCES INDEX