On a subclass of analytic functions for operator on a Hilbert space
Keywords:
Univalent function, coefficient estimates, distortion theorem.Abstract
In this paper we introduce and study a subclass of analytic functions for operators on a Hilbert space in the open unit disk U = fz 2 C : jzj < 1g. We have established coecient estimates, distortion theorem for this subclass, and also an application to operators based on fractional calculus for this class is investigated.
Mathematics Subject Classification (2010): 30C45.
References
Dunford, N., Schwartz, J.T., Linear operators part I. General Theory, New York-London, 1958.
Fan, K., Analytic functions of a proper contraction, Math. Zeitschr., 160(1978), 275-290.
Gupta, V.P., Jain, P.K., A certain classes of univalent functions with negative coefficients, Bull. Austral. Math. Soc., 14(1976), 409-416.
MacGregor, T.H., The radius of convexity for starlike functions of order 1/2 , Proc. Amer. Math. Soc., 14(1963), 71-76.
Owa, S., On the distortion theorem, Kyungpook Math. J., 18(1978), 53-59.
Owa, S., Aouf, M.K., Some applications of fractional calculus operators to classes of univalent functions negative coefficients, Integral Trans. and Special Functions, 3(1995),
no. 3, 211-220.
Robertson, M.S., A characterization of the class of starlike univalent functions, Michigan Math. J., 26(1979), 65-69.
Schild, A., On a class of functions schlicht in the unit circle, Proc. Amer. Math. Soc., 5(1954), 115-120.
Silverman, H., Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51(1975), 109-116.
Xiaopei, Y., A subclass of analytic p-valent functions for operator on Hilbert space, Math. Japon., 40(1994), no. 2, 303-308.
Xia, D., Spectral theory of hyponormal operators, Sci. Tech. Press, Shanghai, 1981, Birkhauser Verlag, Basel-Boston-Stuttgart, 1983, 1-241.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2016 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.