Three families of two-parameter means constructed by trigonometric functionsReport as inadecuate

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Journal of Inequalities and Applications

, 2013:541

First Online: 19 November 2013Received: 16 April 2013Accepted: 10 October 2013


In this paper, we establish three families of trigonometric functions with two parameters and prove their monotonicity and bivariate log-convexity. Based on them, three two-parameter families of means involving trigonometric functions, which include Schwab-Borchardt mean, the first and second Seiffert means, Sándor’s mean and many other new means, are defined. Their properties are given and some new inequalities for these means are proved. Lastly, two families of two-parameter hyperbolic means, which similarly contain many new means, are also presented without proofs.

MSC: 26E60, 26D05, 33B10, 26A48.

Keywordstrigonometric function hyperbolic function mean inequality  Download fulltext PDF

Author: Zhen-Hang Yang



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