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Coefficient discs and generalized central functions for the class of concave schlicht functions
Bappaditya Bhowmik,Karl-Joachim Wirths 대한수학회 2014 대한수학회보 Vol.51 No.5
We consider functions that map the open unit disc confor- mally onto the complement of an unbounded convex set with opening angle πα, α ∈ (1, 2], at infinity. We derive the exact interval for the vari- ability of the real Taylor coefficients of these functions and we prove that the corresponding complex Taylor coefficients of such functions are con- tained in certain discs lying in the right half plane. In addition, we also determine generalized central functions for the aforesaid class of functions.
COEFFICIENT DISCS AND GENERALIZED CENTRAL FUNCTIONS FOR THE CLASS OF CONCAVE SCHLICHT FUNCTIONS
Bhowmik, Bappaditya,Wirths, Karl-Joachim Korean Mathematical Society 2014 대한수학회보 Vol.51 No.5
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.