A refined discrete Hilbert inequality obtained via the HermiteHadamard inequality ?
In this paper we establish a general method for improving the discrete Hilbert-type inequalities via the HermiteHadamard inequality. The general result is then applied to homogeneous kernels. Moreover, some particular homogeneous kernels are considered, and a whole series of refinements of some recent results known from the literature are yielded. In addition some particular non-homogeneous cases are also considered.
hilbert inequality hermitehadamard inequality convexity beta function the incomplete beta function