On Some Extensions of Hardy-Hilbert's Inequality and Applications

On a more accurate half-discrete Hilbert's inequality

“…Inequalities (1)-(3) are important in analysis and its applications [4]. There are lots of improvements, generalizations, and applications of inequalities (1)(2)(3), for more details, refer to literatures [5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

On a more accurate half-discrete mulholland's inequality and an extension

“…Some other results about Hilbert-type inequalities are provided by [8][9][10][11][12][13][14][15][16].…”

A half-discrete Hilbert-type inequality with a homogeneous kernel and an extension

“…Some other results about Hilberttype inequalities are provided by [7][8][9][10][11][12][13][14][15]. On half-discrete Hilbert-type inequalities with the non-homogeneous kernels, Hardy et al provided a few results in Theorem 351 of [1].…”