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For a function f defined in an interval I, satisfying the conditions ensuring the existence and uniqueness of the Lagrange mean L[f], we prove that there exists a unique two variable mean M[f] such thatf(x)−f(y)x−y=M[f](f′(x),f′(y)) for all x,y∈I, x≠y. The mean M[f] is closely related L[f]. Necessary and sufficient condition for the equality M[f]=M[g] is given. A family of means {M[t]:t∈R} relevant...
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