On a more accurate half-discrete multidimensional Hilbert-type inequality involving one derivative function of m-order

Abstract

AbstractBy means of the weight functions, the idea of introduced parameters, using the transfer formula and Hermite–Hadamard’s inequality, a more accurate half-discrete multidimensional Hilbert-type inequality with the homogeneous kernel as $\frac{1}{(x + \Vert k - \xi \Vert _{\alpha} )^{\lambda + m}}\ (x,\lambda > 0)$ 1 ( x + ∥ k − ξ ∥ α ) λ + m ( x , λ > 0 ) involving one derivative function of m-order is given. The equivalent conditions of the best possible constant factor related to several parameters are considered. The equivalent forms. the operator expressions and some particular inequalities are obtained.