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

Namita Das ; Srinibas Sahoo

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2011), pp. 29-44.

Résumé

This paper deals with a generalization of Hardy–Hilbert's inequality for non-homogeneous kernel by considering sequences $(s_n)$, $(t_n)$, the functions ${\varphi }_p$, ${\varphi }_q$ 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.

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