Published in
Elsevier, Journal of Approximation Theory, (174), p. 1-9, 2013
DOI: 10.1016/j.jat.2013.06.005
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Convexity of the generalized sine function and the generalized hyperbolic sine function
Journal article published in 2013 by
Wei-Dong Jiang,
Miao-Kun Wang,
Yu-Ming Chu,
Yue-Ping Jiang,
Feng Qi 
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Abstract
In the paper, the authors prove that the generalized sine function $\sin_{p,q}x$ and the generalized hyperbolic sine function $\sinh_{p,q}x$ are respectively geometrically concave and geometrically convex. Consequently, the authors verify a conjecture posed by B. A. Bhayo and M. Vuorinen.