Authors: | Simić, Slavko | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | On some intermediate mean values | Journal: | International Journal of Mathematics and Mathematical Sciences | Volume: | 2013 | Issue Date: | 15-Mar-2013 | ISSN: | 0161-1712 | DOI: | 10.1155/2013/283127 | Abstract: | We give a necessary and sufficient mean condition for the quotient of two Jensen functionals and define a new class Λf,g (a, b) of mean values where f, g are continuously differentiable convex functions satisfying the relation f ″ (t) = t g ″ (t), t +. Then we asked for a characterization of f, g such that the inequalities H (a, b) ≤ Λf,g (a, b) ≤ A (a, b) or L (a, b) ≤ Λf,g (a, b) ≤ I (a, b) hold for each positive a, b, where H, A, L, I are the harmonic, arithmetic, logarithmic, and identric means, respectively. For a subclass of Λ with g ″ (t) = ts, s, this problem is thoroughly solved. |
Publisher: | Hindawi |
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