SHARP BOUNDS FOR NEUMAN-SANDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS
In this article, we prove that the double inequality αP（a,b）＋（1-α）Q（a,b）〈M（a,b）〈βP（a,b）＋（1-β）Q（a,b） holds for any a,b 〉 0 with a ≠ b if and only if α≥1/2 and β≤[π（√2 lov （1＋√2）-1]/[√2π-2） log （1＋√2）]=0.3595…,where M（a, b）, Q（a, b）, and P（a, b） ave the Neuman-Sandor, quadratic, and first Seiffert mea...
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| Veröffentlicht in: | Acta mathematica scientia 2014-05, Vol.34 (3), p.797-806 |
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| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this article, we prove that the double inequality
αP（a,b）＋（1-α）Q（a,b）〈M（a,b）〈βP（a,b）＋（1-β）Q（a,b）
holds for any a,b 〉 0 with a ≠ b if and only if α≥1/2 and β≤[π（√2 lov （1＋√2）-1]/[√2π-2） log （1＋√2）]=0.3595…,where M（a, b）, Q（a, b）, and P（a, b） ave the Neuman-Sandor, quadratic, and first Seiffert means of a and b, respectively. |
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| ISSN: | 0252-9602 1572-9087 |
| DOI: | 10.1016/S0252-9602(14)60050-3 |