A generalization of Hardy–Hilbert's inequality for non-homogeneous kernel

This paper deals with a generalization of Hardy–Hilbert's inequality for non-homogeneous kernel by considering sequences $(s_n)$, $(t_n)$, the functions $\phi_p$, $\phi_q$ and parameter $\lambda$. This inequality generalizes both Hardy–Hilbert's inequality and Mulholland's inequality, which includes most of the recent results of this type. As applications, the equivalent form, some particular results and a generalized Hardy–Littlewood inequality are established.