LOGARITHMIC COEFFICIENTS OF SOME CLOSE-TO-CONVEX FUNCTIONS
By Md Firoz Ali, A. Vasudevarao. Bulletin of the Australian Mathematical Society, 2016
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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 $f$ .
Subfields: Applied Mathematics, Geometry and Topology, Polymers and Plastics
View Paper: https://www.semanticscholar.org/paper/337d30ab48a276a1ccdb3759abb6db25f02fc774
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In Applied Mathematics
In Geometry and Topology
In Polymers and Plastics
Citations in the corpus
- Second Hankel Determinant of Logarithmic Coefficients of Convex and Starlike Functions of Order Alpha (2021, background): “Logarithmic coefficients have recently attracted considerable interest (see [2, 3, 6, 10, 13, 20]).”