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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