Mean-value theorems and some symmetric means
نویسندگان
چکیده
منابع مشابه
Power Means Generated by Some Mean-value Theorems
According to a new mean-value theorem, under the conditions of a function f ensuring the existence and uniqueness of Lagrange’s mean, there exists a unique mean M such that f(x)− f(y) x− y = M ( f ′(x), f ′(y) ) . The main result says that, in this equality, M is a power mean if, and only if, M is either geometric, arithmetic or harmonic. A Cauchy relevant type result is also presented. Introdu...
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ژورنال
عنوان ژورنال: Demonstratio Mathematica
سال: 2013
ISSN: 2391-4661
DOI: 10.1515/dema-2013-0472