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

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