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

Abstract:

      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.