Fekete-Szegö and Hankel inequalities for certain class of analytic functions related to the sine function

AIMS Mathematics

卷:7

Huo Tang¹  Li-Na Ma¹  Shu-Hai Li¹  Gangadharan Murugusundaramoorthy² 

[1] 1. School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, Inner Mongolia, China;

[2] 2. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632014, Tamilnadu, India;

关键词: analytic function;    starlike function;    subordination;    coefficient problem;    fekete-szegöinequality;    hankel determinant;    poisson distribution series;   

DOI  :  10.3934/math.2022354

来源: DOAJ

【 摘 要 】

In this present investigation, the authors obtain Fekete-Szegö inequality for certain normalized analytic function $ f(\zeta) $ defined on the open unit disk for which$ (f'(\zeta)^{\vartheta}\left( \frac{\zeta f'(\zeta )}{f(\zeta )}\right)^{1-\vartheta} \prec 1+\sin \zeta ; \qquad (0\leq \vartheta \leq 1) $lies in a region starlike with respect to $ 1 $ and symmetric with respect to the real axis. As a special case of this result, the Fekete-Szegö inequality for a class of functions defined through Poisson distribution series is obtained. Further, we discuss the second Hankel inequality for functions in this new class.

【 授权许可】

Unknown