Convexity of the generalized sine function and the generalized hyperbolic sine function

In the paper, the authors prove that the generalized sine function sinp,qx and the generalized hyperbolic sine function sinhp,qx are respectively geometrically concave and geometrically convex. Consequently, the authors verify a conjecture posed by B. A. Bhayo and M. Vuorinen.

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Veröffentlicht in:Journal of approximation theory Jg. 174; S. 1 - 9
Hauptverfasser: Jiang, Wei-Dong, Wang, Miao-Kun, Chu, Yu-Ming, Jiang, Yue-Ping, Qi, Feng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.10.2013
Schlagworte:
Conjecture
Generalized hyperbolic sine
Generalized sine
Geometric convexity
Inequality
Generalized hyperbolic sine
Geometric convexity
Generalized sine
Conjecture
Inequality
ISSN:0021-9045, 1096-0430
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Zusammenfassung:In the paper, the authors prove that the generalized sine function sinp,qx and the generalized hyperbolic sine function sinhp,qx are respectively geometrically concave and geometrically convex. Consequently, the authors verify a conjecture posed by B. A. Bhayo and M. Vuorinen.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2013.06.005