On a half-discrete Hardy-Hilbert’s inequality involving one multiple upper limit function

Abstract

Abstract: By means of the weight functions, Hermite-Hadamard’s inequality, and the method of real analysis, a new and more accurate half-discrete Hardy-Hilbert’s inequality involving one multiple upper limit function is given. As applications, the equivalent conditions of the best possible constant factor related to a few parameters in the new inequality and some particular inequalities for taking special parameter values are further explored and demonstrated.

Key words: weight function, Hermite-Hadamard’s inequality, half-discrete Hardy-Hilbert’s inequality, multiple upper limit function, parameter, best possible constant factor

CLC Number:

O178

WANG Ai-zhen, YANG Bi-cheng. On a half-discrete Hardy-Hilbert’s inequality involving one multiple upper limit function[J]. Journal of Lanzhou University of Technology, 2025, 51(6): 167-172.

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