On an integral operator of meromorphic functions

Abstract

New sufficient conditions are derived for the integraloperator of mereomorphic functions defined by$$H(z)=\frac{c}{z^{c+1}}ınt_{0}^{z}u^{c-1}(uf_{1}(u))^{\gamma_{1}}\dotsm(uf_{n}(u))^{\gamma _{n}}\,du,$$to be in the class $\Sigma_{N}(\lambda)$ of meromorphic functionssatisfying the condition $-\Re\{\frac{zf^{\prime \prime}(z)}{f^{\prime}(z)}+1\}<\lambda$, where $\lambda>1$.