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- W2549300911 abstract "Let the function $f$ be analytic in $mathbb{D}={z:|z|<1}$ and given by $f(z)=z+sum _{n=2}^{infty }a_{n}z^{n}$ . For $0<unicode[STIX]{x1D6FD}leq 1$ , denote by ${mathcal{C}}(unicode[STIX]{x1D6FD})$ the class of strongly convex functions. We give sharp bounds for the initial coefficients of the inverse function of $fin {mathcal{C}}(unicode[STIX]{x1D6FD})$ , showing that these estimates are the same as those for functions in ${mathcal{C}}(unicode[STIX]{x1D6FD})$ , thus extending a classical result for convex functions. We also give invariance results for the second Hankel determinant $H_{2}=|a_{2}a_{4}-a_{3}^{2}|$ , the first three coefficients of $log (f(z)/z)$ and Fekete–Szegö theorems." @default.
- W2549300911 created "2016-11-30" @default.
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- W2549300911 date "2016-11-23" @default.
- W2549300911 modified "2023-09-29" @default.
- W2549300911 title "INVARIANCE OF THE COEFFICIENTS OF STRONGLY CONVEX FUNCTIONS" @default.
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- W2549300911 doi "https://doi.org/10.1017/s0004972716000976" @default.
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