The author considers generalized Jacobian elliptic functions. The inverse function of the generalized Jacobian elliptic sine function \(sn^{-1}_{p,q}(x)\) is defined as \( sn^{-1}_{p,q}(x)=\int_0^x((1-w^q)(1-k^qw^q))^{-1/p}dw\) and subordinated functions to \(sn_{p,q}\) are defined as \(\displaystyle cn_{p,q}(t)= (1-sn_{p,q}^q(t))^{1/p}\), \(dn_{p,q}(t)= (1-k^qsn_{p,q}^q(t))^{1/p}\). Assume that \(p\) and \(q\) satisfy the conditions \(p,q>1\) and \(p(q+1)-2q>0\), then \[ \frac1{sn_{p,q}(t)}=R_N(cn_{p,q}^p(t),dn_{p,q}^p(t),1), \] where \(R_N=R_{-1/q}(b;X)\) is the \(R\)-hypergeometric function and \(b=(1/p,1/p,1+1/q-2/p)\) (Theorem 3.1). Certain inequalities involving generalized Jacobian elliptic functions are obtained in Theorem 3.2. If \(p\) and \(q\) satisfy conditions of Theorem 3.1, then the function \(sn_{p,q}(t)\) is multiplicatively concave (\(f\) is multiplicatively concave if \(\displaystyle f(x^\alpha y^\beta)\geq f(x)^\alpha f(y)^\beta)\) for \(\alpha+\beta=1\)) (Theorem 3.6). In Theorem 3.9 it is proved that \(sn_{p,q}(t)/t>1/sn^{-1}_{p,q}(t)\).