Difference between revisions of "Cauchy Functional Equation"
Revision as of 06:06, 29 March 2008
The Cauchy Functional Equation refers to the functional equation , with for all .
If (or any subset closed to addition like or ), the solutions are only the functions , with .
If , then we need a suplementar condition like continous, or monotonic, or for all , to get that all the solutions are of the form , with .
There have been given examples of real functions that fulfill the Cauchy Functional Equation, but are not linear, which use advanced knowledge of real analysis.
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