Coefficient discs and generalized central functions for the class of concave schlicht functions
Bull. Korean Math. Soc. 2014 Vol. 51, No. 5, 1551-1559
Printed September 30, 2014
Bappaditya Bhowmik and Karl-Joachim Wirths
Indian Institute of Technology Kharagpur, Institut f\"ur Analysis and Algebra
Abstract : We consider functions that map the open unit disc conformally onto the complement of an unbounded convex set with opening angle $\pi\alpha$, $\alpha\in (1,2],$ 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
MSC numbers : 30C45
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