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This note addresses monotonic growths and logarithmic convexities of the weighted((1-t2)αdt2,-∞<α<∞,0<t<1)integral means Aα,β(f,)and Lα,β(f,)of the mixed area(πr2)-βA(f,r)and the mixed length(2πr)-βL(f,r)(0≤β≤1 and0<r<1)of f(rD)and f(rD