Third Order Hankel Determinant for the Inverse of Starlike and Convex Functions

doi:10.13438/j.cnki.jdzk.2021.02.003

Abstract

Abstract: Let S* be the class of functions f univalent in the unit disk Δ={z:|z|<1} such that Re zf′(z)〖〗f(z)>0 (z∈Δ) and let K be the class of functions f univalent in the unit disk Δ={z:|z|<1} such that Re (1+zf″(z)〖〗f′(z))>0 (z∈Δ). Using Toeplitz determinant, we obtian the upper bound of the third order Hankel determinants for the inverse functions of f∈S* and f∈K.

Key words: univalent function, starlike function, convex function, third Hankel determinant, inverse function, upper bound

SONG Yuan. Third Order Hankel Determinant for the Inverse of Starlike and Convex Functions[J]. Journal of Jishou University(Natural Sciences Edition), 2021, 42(2): 12-19.

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