Advertisement

Functional equations with two variables

Chapter
  • 3.4k Downloads
Part of the Problem Books in Mathematics book series (PBM)

Abstract

Let us begin by restating and solving Cauchy’s functional equation. Let f : RR be a continuous function satisfying
$$ f\left( {x + y} \right) = f\left( x \right) + f\left( y \right) $$
(2.1)
for all real x and y. We show that there exists a real number a such that f(x) = ax for all xR.

Keywords

Continuous Function Real Number Functional Equation Rational Number Trigonometric Identity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media, LLC 2007

Personalised recommendations