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AbstractBy means of weight coefficients and the technique of real analysis, a new Hardy-Mulholland-type inequality with the kernel Kλ(m,n):=1lnλUm+lnλVn+α|lnλUm−lnλVn|$$ K_{\lambda}(m,n):=\frac{1}{\ln^{\lambda}U_{m}+\ln^{\lambda }V_{n}+\alpha |\ln^{\lambda}U_{m}-\ln^{\lambda}V_{n}|} $$ (−1<α≤1$-1<\alpha\leq1$, 0<λ≤2$0<\lambda\leq2$; m,n∈N∖{1}$m,n\in\mathbf{N}\backslash\{ 1\}$) and a best possible constant factor is provided, which is a relation between two simple Hardy-Mulholland-type inequalities with parameters. The equivalent forms, the operator expression with the norm, and some particular inequalities are studied. The lemmas and theorems of this paper provide an extensive account of this type of inequalities.

A relation between two simple Hardy-Mulholland-type inequalities with parameters