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MEAN-VALUE PROPERTY AND CHARACTERIZATIONS OF SOME ELEMENTARY FUNCTIONS
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 Title & Authors
MEAN-VALUE PROPERTY AND CHARACTERIZATIONS OF SOME ELEMENTARY FUNCTIONS
Matkowski, Janusz;
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 Abstract
A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation , where M is a given mean and , F, , G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.
 Keywords
mean-value theorem;classical means;monotonic functions;quadratic function;homographic function;square root function;functional equation;
 Language
English
 Cited by
 References
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