Optimal Bounds for the Neuman-Sándor Mean in terms of the Convex Combination of the First and Second Seiffert Means

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2015 English Publisher:Hindawi LimitedJournal:Mathematical Problems in Engineering, volume 2,015, pages 1-6 (issn: 1024-123X, eissn: 1563-5147,

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Authors: Cui, Hao-Chuan; Wang, Nan; Long, Bo-Yong;

doi: 10.1155/2015/489490

Optimal Bounds for the Neuman-Sándor Mean in terms of the Convex Combination of the First and Second Seiffert Means

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Abstract

We find the least valueαand the greatest valueβsuch that the double inequalityαP(a,b)+(1-α)T(a,b)<M(a,b)<βP(a,b)+(1-β)T(a,b)holds for alla,b>0witha≠b, whereM(a,b), P(a,b), andT(a,b)are the Neuman-Sándor mean and the first and second Seiffert means of two positive numbersaandb, respectively.

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Anhui University
China (People's Republic of)

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