engleski

A refined discrete Hilbert inequality via the Hermite-Hadamard inequality

In this paper we establish a general method for improving the discrete Hilbert-type inequalities via the Hermite-Hadamard inequality. The general result is then applied to homogeneous kernels. Moreover, some particular homogeneous kernels are considered, which yields the whole series of refinements of some recent results known from the literature. In addition some particular non-homogeneous cases are also considered.

Hilbert inequality; Hermite-Hadamard inequality; convexity; Beta function; the incomplete Beta function

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