Zalcman conjecture and Hankel determinant of order three for starlike and convex functions associated with shell-like curves

V. Suman Kumar ; R. Bharavi Sharma

Problemy analiza, Tome 9 (2020) no. 2, pp. 119-137.

Résumé

The aim of this article is to estimate an upper bound of $|H_3(1)|$, the Zalcman coefficient functional for $n=3$ and $n=4$, and also to investigate the fifth, sixth, seventh coefficients of starlike and convex functions associated with shell-like curves. Similar type of outcomes are estimated for the functions $f^{-1} $ and $\frac{z}{f\left(z\right)}$.

Détail

Keywords: analytic function, function with positive real part, starlike function, Zalcman conjecture, shell-like curve, Hankel determinant.
Mots-clés : subordination

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