Coefficient discs and generalized central functions for the class of concave schlicht functions
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
Abstract
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.
참고문헌 (11)
- F. G. Avkhadiev, "Sharp inequalities for the coefficients of concave schlicht functions", Comment. Math. Helv, 81(4), pp.801~807 (2006)
- F. G. Avkhadiev, "Concave schlicht functions with bounded opening angle at infinity", Lobachevskii J. Math, 17, pp.3~10 (2005)
- U. Bednarz, "On T-neighborhoods of analytic functions", J. Math. Appl, 32, pp.25~32 (2010)
- B. Bhowmik, "On concave univalent functions", Math. Nachr, 285(5-6), pp.606~612 (2012)
- B. Bhowmik, "Characterization and the pre-Schwarzian norm estimate for concave univalent functions", Monatsh. Math, 161(1), pp.59~75 (2010)
- B. Bhowmik, "Central functions for classes of concave univalent functions", Math. Slovaca
- W. Rogosinski, "Uber positive harmonische Entwicklungen und typisch reelle Potenzreihen", Math. Z, 35(1), pp.93~121 (1932)
- St. Ruscheweyh, "Neighborhoods of univalent functions", Proc. Amer. Math. Soc, 81(4), pp.521~527 (1981)
- T. Sheil-Small, "On the convolution of analytic functions", J. Reine Angew. Math, 258, pp.137~152 (1973)
- T. Sheil-Small, "Neighborhoods of analytic functions", J. Analyse Math, 52, pp.210~240 (1989)
- J. Sok´ol, "On neighborhoods of analytic functions with positive real part", Math. Nachr, 284(11-12), pp.1547~1553 (2011)