Abstract: By using  the weight function method, the Euler-Maclaurin summation formula, Abel’s summation by parts formula and the differential mean value theorem, we gave a new half-discrete Mulholland-type inequality involving  multiple upper limit function and  partial sums, and discussed the equivalence  of the best constant factor with multiple parameters in the new inequality.

Key words: weight coefficient, parameter, half-discrete Mulholland-type inequality, Euler-Maclaurin summation formula, partial sums, Abel’s , summation by parts formula