Optimal one-parameter mean bounds for the convex combination of arithmetic and geometric means

• Autorzy: Xia W. , Hou S. , Wang G. , Chu Y.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we answer the question: What are the greatest value p = p(α) and least value q = q(α)such that the double inequality Jp(a,b) < αA(a,b) + (1 - α)G(a,b) < Jq(a,b) holds for any α ∈ (0,1) and all a,b > 0 with a ≠ b? Here, A(a,b) = (a+b):2, G(a,b) = √ab and Jp (a,b) denote the arithmetic, geometric and p-th one-parameter means of a and b, respectively.

Słowa kluczowe

EN

one-parameter mean; arithmetic mean; geometric mean

PL

średnia arytmetyczna; średnia geometryczna

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2012
• Tom: Vol. 18, nr 2
• Strony: 197--207
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Xia W.

autor

Hou S.

autor

Wang G.

autor

Chu Y.

• School of Teacher Education, Huzhou Teachers College, Huzhou 313000, China,

Bibliografia

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