The norm of pre-Schwarzian derivatives of certain analytic functions with bounded positive real part
Keywords:
Univalent functions, starlike functions, subordination, pre-Schwarzian derivatives.Abstract
For real numbers 0 < 1 and > 1 we define the univalent function in the unit disk which maps on to the strip domain ! with < Re ! < .In this paper we give the best estimates for the norm of the pre-Schwarzian derivative Tf (z) =f00(z)f0 (z)where kTf k = supjzj<1
Mathematics Subject Classification (2010): 30C45.
References
Becker, J., Lownersche dfferentialgleichung and quasikonform fortsetzbare schlichte funktionen, J. Reine Angew. Math, 255(1972), 23-43.
Becker, J. Pommerenke, Ch., Schlichtheit-skriterien und jordangebiete, J. Reine Angew. Math, 354(1984), 74-94.
Duren, P.L., Univalent functions, Springer, New York, 1978.
Kim, Y.C. Sugawa, T., Norm estimates of the pre-Schwarzian derivatives for certain classes of univalent functions, Proc. Edinburgh Math. Soc, 49(2006), 131{143.
Kuroki, K. Owa, S., Notes on new class for certain analytic functions, Advances in Mathematics: Scientific. Journal 1, 2(2012), 127-131.
Miller, S.S, Mocanu, P.T., Di_erential subordinations, theory and applications, Marcel Dekker, 2000.
Okuyama, Y., The norm estimates of pre-Schwarzian derivatives of spiral-like functions, Complex Var. Theory Appl, 42(2000), 225-239.
Yamashita, S., Norm estimates for function starlike or convex of order alpha, Hokkaido Mathematical Journal, 28(1999), 217-230.
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