On an integral operator of meromorphic functions

Abstract

New sufficient conditions are derived for the integraloperator of mereomorphic functions defined by$$H(z)=\frac{c}{z^{c+1}}ın{t}_0^z{u}^{c-1}(u{f}_1(u){)}^{{\gamma }_1}\cdots (u{f}_n(u){)}^{{\gamma }_n}du,$$to be in the class ${\mathrm{\Sigma }}_N(\lambda )$ of meromorphic functionssatisfying the condition $-\mathrm{\Re }\{\frac{z{f}^{\prime \prime }(z)}{f^{\prime }(z)}+1\}<\lambda$, where $\lambda >1$.