Abstract and Applied Analysis

Best Possible Bounds for Neuman-Sándor Mean by the Identric, Quadratic and Contraharmonic Means

Tie-Hong Zhao, Yu-Ming Chu, Yun-Liang Jiang, and Yong-Min Li

Full-text: Open access

Abstract

We prove that the double inequalities I α 1 ( a , b ) Q 1 - α 1 ( a , b ) < M ( a , b ) < I β 1 ( a , b ) Q 1 - β 1 ( a , b ) , I α 2 ( a , b ) C 1 - α 2 ( a , b ) < M ( a , b ) < I β 2 ( a , b ) C 1 - β 2 ( a , b ) hold for all a , b > 0 with a b if and only if α 1 1 / 2 , β 1 log [ 2 log ( 1 + 2 ) ] / ( 1 - log 2 ) , α 2 5 / 7 , and β 2 log [ 2 log ( 1 + 2 ) ] , where I ( a , b ) , M ( a , b ) , Q ( a , b ) , and C ( a , b ) are the identric, Neuman-Sándor, quadratic, and contraharmonic means of a and b , respectively.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 348326, 12 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511798

Digital Object Identifier
doi:10.1155/2013/348326

Mathematical Reviews number (MathSciNet)
MR3035385

Zentralblatt MATH identifier
1276.26065

Citation

Zhao, Tie-Hong; Chu, Yu-Ming; Jiang, Yun-Liang; Li, Yong-Min. Best Possible Bounds for Neuman-Sándor Mean by the Identric, Quadratic and Contraharmonic Means. Abstr. Appl. Anal. 2013 (2013), Article ID 348326, 12 pages. doi:10.1155/2013/348326. https://projecteuclid.org/euclid.aaa/1393511798


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