On a subclass of analytic functions for a operator on Hilbert Space
Keywords:
univalent function, coefficient estimates, distortion theorem,Abstract
In this paper we introduce and study a subclass of analyticfunctions 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.
References
N. Dunford and J. T. Schwartz, Linear operators part I. General Theory, New
York-London, (1958).
K. Fan, Analytic functions of a proper contraction, Math. Zeitschr., 160(1978),
-290.
V. P. Gupta , P. K. Jain, A certain classes of univalent functions with negative
coecients, Bull. Austral. Math. Soc., 14(1976), 409-416.
T. H. MacGregor, The radius of convexity for starlike functions of order 1
,
Proc. Amer. Math. Soc., 14(1963), 71-76.
S. Owa, On the distortion theorem, Kyungpook Math. J. , 18(1978), 53-59.
S. Owa, M. K. Aouf, Some applications of fractional calculus operators to
classes of univalent functions negative coecients, Integral Trans.and Special
Functions, 3(1995), no. 3 211-220.
M. S. Robertson, A characterization of the class of starlike univalent functions,
Michigan Math. J., 26(1979), 65-69.
A. Schild, On a class of functions schlicht in the unit circle, Proc. Amer. Math.
Soc. 5(1954), 115-120.
H. Silverman, Univalent functions with negative coecients, Proc. Amer. Math.
Soc., 51(1975), 109-116.
Y. Xiaopei, A subclass of analytic p-valent functions for operator on Hilbert
space, Math. Japon., 40(1994), no. 2 303-308.
D. Xia, Spectral theory of hyponormal operators, Sci. Tech. Press, Shanghai,
(1981), Birkhauser Verlag, Basel-Boston-Stuttgart, (1983), 1-241.
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