Malaysian Journal of Mathematical Sciences, October 2014, Vol. 8(S)
Special Issue: International Conference on Mathematical Sciences and Statistics 2013 (ICMSS2013)
Integral Operators Preserving Univalence
Oqlah Al-Refai
Corresponding Email: [email protected]
Received date: -
Accepted date: -
Abstract:
We introduce two new integral operators $F_{\alpha, \beta}$ and $H_{\alpha, \beta, \gamma}$ acting on the class of normalized analytic functions $\mathcal{A}$, where $\alpha, \beta$ and $\gamma$ are complex parameters. Indeed, we derive sufficient conditions on the parameters $\alpha, \beta$ and $\gamma$ to obtain that $F_{\alpha, \beta}(g)$ and $H_{\alpha, \beta, \gamma}(g)$ are univalent functions in the open unit disk $\mathbb{U}$, whenever $g$ is univalent in $\mathbb{U}$.
Keywords: Univalent functions, univalence criteria, integral operators, preserving univalence
