Abstract

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

Keywords: Meromorphic functions; integral operator

MSC: 30C45

Pages:  167$-$172     

Volume  64 ,  Issue  2 ,  2012