[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2015.52.6.1937

FEKETE-SZEGÖ PROBLEM FOR CERTAIN SUBCLASSES OF UNIVALENT FUNCTIONS

VASUDEVARAO, ALLU (Department of Mathematics Indian Institute of Technology Khargpur)

Publication Information

Bulletin of the Korean Mathematical Society / v.52, no.6, 2015 , pp. 1937-1943 More about this Journal

Abstract

For $$1{\leq}{\alpha}$ < $2$$ , let $\mathcal{F}({\alpha})$ denote the class of locally univalent normalized analytic functions $f(z)=z+{\Sigma}_{n=2}^{\infty}{a_nz^n}$ in the unit disk $${\mathbb{D}}=\{z{\in}{\mathbb{C}}:{\left|z\right|}$ < $1\}$$ satisfying the condition $$Re$1+{\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}}$$ > ${\frac{{\alpha}}{2}}-1$$ . In the present paper, we shall obtain the sharp upper bound for Fekete- $Szeg{\ddot{o}}$ functional $|a_3-{\lambda}a_2^2|$ for the complex parameter ${\lambda}$ .

Keywords

univalent functions; starlike; convex; close-to-convex and Fekete- $Szeg{\ddot{o}}$ problem;

Citations & Related Records

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