New Means of Cauchy’s Type
نویسندگان
چکیده
We will introduce new means of Cauchy’s type M r,l f, μ defined, for example, as M s r,l f, μ l l− s /r r − s M r f, μ −Mr s f, μ /M l f, μ −Ml s f, μ 1/ r−l , in the case when l / r / s, l, r / 0. We will show that this new Cauchy’s mean is monotonic, that is, the following result. Theorem. Let t, r, u, v ∈ R, such that t ≤ v, r ≤ u. Then for M r,l f, μ , one has M t,r ≤ M v,u. We will also give some related comparison results.
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