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ON CERTAIN CLOSE-TO-CONVEX FUNCTIONS.
- Source :
-
Bulletin of the Australian Mathematical Society . Apr2024, Vol. 109 Issue 2, p365-375. 11p. - Publication Year :
- 2024
-
Abstract
- Let $\mathcal {K}_u$ denote the class of all analytic functions f in the unit disk $\mathbb {D}:=\{z\in \mathbb {C}:|z| , normalised by $f(0)=f'(0)-1=0$ and satisfying $|zf'(z)/g(z)-1| in $\mathbb {D}$ for some starlike function g. Allu, Sokól and Thomas ['On a close-to-convex analogue of certain starlike functions', Bull. Aust. Math. Soc. 108 (2020), 268–281] obtained a partial solution for the Fekete–Szegö problem and initial coefficient estimates for functions in $\mathcal {K}_u$ , and posed a conjecture in this regard. We prove this conjecture regarding the sharp estimates of coefficients and solve the Fekete–Szegö problem completely for functions in the class $\mathcal {K}_u$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00049727
- Volume :
- 109
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Australian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 175959494
- Full Text :
- https://doi.org/10.1017/S0004972723000655