The Schur-Convexity of the Generalized Muirhead-Heronian Means

Deng, Yong-Ping; Wu, Shan-He; Chu, Yu-Ming; He, Deng

doi:10.1155/2014/706518

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The Schur-Convexity of the Generalized Muirhead-Heronian Means

Author(s): Yong-Ping Deng , Shan-He Wu , Yu-Ming Chu , Deng He

Publication date Created: 2014

Publication date (Print): 2014

Journal: Abstract and Applied Analysis

Publisher: Hindawi Limited

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Abstract

We give a unified generalization of the generalized Muirhead means and the generalized Heronian means involving three parameters. The Schur-convexity of the generalized Muirhead-Heronian means is investigated. Our main result implies the sufficient conditions of the Schur-convexity of the generalized Heronian means and the generalized Muirhead means.