On a Discrete Hilbert Type Inequality With Non–Homogeneous Kernel

New extensions are given for the discrete Hilbert type inequality with non–homogeneous kernel. By this, recently published results by Pogány have been improved by a Hilbert type inequalities in homogeneous kernel case derived by Krnić and Pečarić. Mathematical tools also used are the Dirichlet series’ Laplace–integral representation and the classical Hölder inequality. 2000 Mathematics Subject Classification. Primary 26D15; Secondary 40B05, 40G99