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This note addresses monotonic growths and logarithmic convexities of theweighted ($(1-t^2)^\alpha dt^2$, $-\infty<\alpha<\infty$, $0<t<1$) integralmeans $\mathsf{A}_{\alpha,\beta}(f,\cdot)$ and$\mathsf{L}_{\alpha,\beta}(f,\cdot)$ of the mixed area $(\pir^2)^{-\beta}A(f,r)$ and the mixed length $(2\pi r)^{-\beta}L(f,r)$($0\le\beta\le 1$ and $0<r<1$) of $f(r\mathbb D)$ and $\partial f(r\mathbb D)$under a holomorphic map $f$ from the unit disk $\mathbb D$ into the finitecomplex plane $\mathbb C$.

Weighted Integral Means of Mixed Areas and Lengths under Holomorphic Mappings