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Let Pn,r (x) be the generalized weighted means. Let F( x) be a C 1 function, y = y(x) an implicit decreasing function defined by f( x, y)= 0 and 0 <m<M ≤ m  , n ≥ 2, xi ∈ (m, M), yi ∈ (m  ,M  ). Then for −1 ≤ r ≤ 1, if f  x /f  y ≤ 1, |(F (Pn,1(y)) − F( Pn,r (y)))/(F (Pn,1(x)) − F( Pn,r (x)))| <( maxm ≤ξ≤M |F  (ξ)|)/(minm≤η≤M |F  (η)|) · M/m  . A similar result exists for f  x /f  y ≥ 1. By specifying f( x, y)and F( x), we get various generalizations of Ky Fan's inequality. We also present some results on the comparison of P α n,s (y) − P α n,r (y) and P α n,s (x) − P α n,r (x) for s ≥ r , α ∈ R.

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