Let $H(U)$ be the space of all analytic functions in the unit disk $U$ and let $K subset H(U)$. For the operator $A_{eta,gamma} : K longrightarrow H(U)$ defined by $$ A_{eta,gamma}(f)(z) = [frac{z^gamma}{eta + gamma} int_{0}^{z} f^eta (t)t^{gamma-1} dt]^{1/eta} $$ and $eta,gamma in C$, we determined conditions on g(z), $eta and gamma$ such that $$ z[frac{z}{f(z)]^eta prec z[frac{z}{g(z)]^eta implies z[frac{z}{A_{eta,gamma}(f)(z)]^eta prec z[frac{z}{A_{eta,gamma}(g)(z)]^eta $$ and we presented some particular cases of our main result.