1. ON CERTAIN CLOSE-TO-CONVEX FUNCTIONS.
- Author
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ALI, MD FIROZ and NUREZZAMAN, MD
- Subjects
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ANALYTIC functions , *STAR-like functions , *UNIVALENT functions , *CONVEX functions , *PROBLEM solving , *MATHEMATICS - 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]
- Published
- 2024
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