×

zbMATH — the first resource for mathematics

Optimal convex combination bounds of Seiffert and geometric means for the arithmetic mean. (English) Zbl 1225.26061
Summary: We find the greatest value \(\alpha \) and the least value \(\beta \) such that the double inequality \(\alpha T(a,b) + (1 - \alpha )G(a,b) < A(a,b) < \beta T(a,b) + (1 - \beta )G(a,b)\) holds for all \(a,b > 0\) with \(a \neq b\). Here \(T (a,b), G(a,b)\), and \(A(a,b)\) denote the Seiffert, geometric, and arithmetic means of two positive numbers \(a\) and \(b\), respectively.

MSC:
26E60 Means
PDF BibTeX XML Cite
Full Text: DOI Link