Salagean算子定义的双单叶函数子类的系数估计

Coefficient Bounds for a New Subclass of Bi-Univalent Functions Defined by Salagean Operator

中文关键词:  解析函数  单叶函数  双单叶函数  系数估计  Salagean算子

英文关键词:analytic functions  univalent functions  bi-univalent functions  coefficient bounds  Salagean operator

中文摘要:

      本文利用Salagean算子定义了单位圆盘上的一类双单叶解析函数子类$\mathcal {N}^{h,p}_{\Sigma}(m,\lambda,\mu)$,利用微分从属定理研究得到了它的系数$|a_{2}|$和$|a_{3}|$的上界估计.同时,我们还验证了Brannan和Clunie关于双单叶函数$|a_{2}|\leq\sqrt{2}$的猜想.本文的结果推广了目前的一些研究结果.

英文摘要:

      In this paper, a new subclass $\mathcal {N}^{h,p}_{\Sigma}(m,\lambda,\mu)$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$ is defined by salagean operator. We obtain coefficients bounds $|a_{2}|$ and $|a_{3}|$ for functions of the class. Moreover, we verify Brannan and Clunie's conjecture $|a_{2}|\leq\sqrt{2}$ for some of our classes. The results in this paper extend many results recently researched by many authors.