Abstract and Applied Analysis

Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean

Zai-Yin He, Wei-Mao Qian, Yun-Liang Jiang, Ying-Qing Song, and Yu-Ming Chu

Full-text: Open access

Abstract

We give the greatest values r 1 , r 2 and the least values s 1 , s 2 in (1/2, 1) such that the double inequalities C ( r 1 a + ( 1 - r 1 ) b , r 1 b + ( 1 - r 1 ) a ) < α A ( a , b ) + ( 1 - α ) T ( a , b ) < C ( s 1 a + ( 1 - s 1 ) b , s 1 b + ( 1 - s 1 ) a ) and C ( r 2 a + ( 1 - r 2 ) b , r 2 b + ( 1 - r 2 ) a ) < α A ( a , b ) + ( 1 - α ) M ( a , b ) < C ( s 2 a + ( 1 - s 2 ) b , s 2 b + ( 1 - s 2 ) a ) hold for any α ( 0,1 ) and all a , b > 0 with a b , where A ( a , b ) , M ( a , b ) , C ( a , b ), and T ( a , b ) are the arithmetic, Neuman-Sándor, contraharmonic, and second Seiffert means of a and b , respectively.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 903982, 5 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511799

Digital Object Identifier
doi:10.1155/2013/903982

Mathematical Reviews number (MathSciNet)
MR3035386

Zentralblatt MATH identifier
1272.26030

Citation

He, Zai-Yin; Qian, Wei-Mao; Jiang, Yun-Liang; Song, Ying-Qing; Chu, Yu-Ming. Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean. Abstr. Appl. Anal. 2013 (2013), Article ID 903982, 5 pages. doi:10.1155/2013/903982. https://projecteuclid.org/euclid.aaa/1393511799


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