Mean-value type equalities with interchanged function and derivative
2011
scientific article
english
- mean value theorem
- mean
EN According to a new mean value-theorem, if a func¬tion f satisfies the classical conditions ensuring the existence and uniqueness of Lagrange’s mean, then there also exists a unique mean M such that ((f(x) – f(y))/(x – y)) = M (f'(x); f'(y)). The main result gives necessary and sufficient conditions for the equality ((f'(x) – f'(y))/(x – y)) = M (f(x); f(y)). The relevant equality for the Lagrange mean-value theorem is also considered.
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