f-0-1-R-g-0-1-N-R-g-n-x-f-g-n-1-x-g-0-x-x-A-f-n-0-1-f-t-g-n-t-dt-A-f-g-A-f-A-g-A-kf-kA-f-

Question Number 1055 by 123456 last updated on 24/May/15

f : [0, 1] \to R

g : [0, 1] \times N \to R

g_{n} (x) = f [g_{n - 1} (x)]

g_{0} (x) = x

A {f} (n) = \underset{0}{\int^{1}} f (t) g_{n} (t) d t

A {f + g} \overset{?}{=} A {f} + A {g}

A {k f} \overset{?}{=} k A {f}