A function \(f: I\to J\) is called \(H_{p,q}\)-convex, if \(f(H_p(x,y))\leq H_q(f(x),f(y))\) for any \(x\), \(y\) in \(I\), where \(H_k\) denotes the Hölder mean of order \(k\). Let \({\mathcal K}={\mathcal K}(r)\) be the complete elliptic integral of the first kind. By using the monotone form of l'Hôpital's rule, the author proves that the composition of inverse hyperbolic tangent function and Jacobian sine function \(\operatorname{arth}\operatorname{sn}\) is strictly \(H_{p,q}\)-convex on \((o,{\mathcal K})\) iff \((p,q)\in\{(p,q): q\geq D(p)\}\), where \(D(p)= p\) if \(p\geq 1\), and \(D(p)= C(p-1)+1\) for \(p<1\), where \(C(p)\) is a certain function of \(p\) (explicitly given) continuous and strictly increasing in \(p\) and \(C(-1)= -1\).