COEFFICIENT DISCS AND GENERALIZED CENTRAL FUNCTIONS FOR THE CLASS OF CONCAVE SCHLICHT FUNCTIONS

Title & Authors
COEFFICIENT DISCS AND GENERALIZED CENTRAL FUNCTIONS FOR THE CLASS OF CONCAVE SCHLICHT FUNCTIONS
Bhowmik, Bappaditya; Wirths, Karl-Joachim;

Abstract
We consider functions that map the open unit disc conformally onto the complement of an unbounded convex set with opening angle $\small{{\pi}{\alpha}}$, $\small{{\alpha}{\in}(1,2]}$, at infinity. We derive the exact interval for the variability of the real Taylor coefficients of these functions and we prove that the corresponding complex Taylor coefficients of such functions are contained in certain discs lying in the right half plane. In addition, we also determine generalized central functions for the aforesaid class of functions.
Keywords
concave function with bounded opening angle at infinity;coefficient region;generalized central functions;
Language
English
Cited by
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