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Equivalent Property of a More Accurate Half-Discrete Hilbert’s Inequality
Bicheng Yang,Aizhen Wang
Keywords:weight function; half-discrete Hilbert’s inequality; equivalent statement; Hermite-Hadamard’s inequality.
Abstract:
      By using the weight functions, the idea of introducing parameters, and Hermite-Hadamard’s inequality, a more accurate half-discrete Hilbert’s inequality with the nonhomogeneous kernel and its equivalent form are given. The equivalent statements of the best possible constant factor related to parameters, the operator expressions and some particular cases are considered. The cases of the relating homogeneous kernel are also deduced.