101. LOGARITHMIC COEFFICIENTS OF SOME CLOSE-TO-CONVEX FUNCTIONS.
- Author
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ALI, MD FIROZ and VASUDEVARAO, A.
- Subjects
LOGARITHMIC functions ,CONVEX functions ,ANALYTIC functions ,UNIVALENT functions ,STAR-like functions ,MATHEMATICAL inequalities - Abstract
The logarithmic coefficients $\unicode[STIX]{x1D6FE}_{n}$ of an analytic and univalent function $f$ in the unit disc $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ with the normalisation $f(0)=0=f^{\prime }(0)-1$ are defined by $\log (f(z)/z)=2\sum _{n=1}^{\infty }\unicode[STIX]{x1D6FE}_{n}z^{n}$. In the present paper, we consider close-to-convex functions (with argument 0) with respect to odd starlike functions and determine the sharp upper bound of $|\unicode[STIX]{x1D6FE}_{n}|$, $n=1,2,3$, for such functions $f$. [ABSTRACT FROM PUBLISHER]
- Published
- 2017
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