On a subclass of analytic functions for operator on a Hilbert space

Authors

  • Sayali JOSHI Department of Mathematics, Sanjay Bhokare Group of Institutes, Miraj Miraj 416410, India e-mail: joshiss@sbgimiraj.org
  • Santosh B. JOSHI Department of Mathematics, Walchand College of Engineering Sangli 416415, India e-mail: joshisb@hotmail.com
  • Ram MOHAPATRA Department of Mathematics, University of Central Florida Orlando, F.L. U.S.A. e-mail: ramm1627@gmail.com https://orcid.org/0000-0002-5502-3934

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

2016-06-30

How to Cite

JOSHI, S., JOSHI, S. B., & MOHAPATRA, R. (2016). On a subclass of analytic functions for operator on a Hilbert space. Studia Universitatis Babeș-Bolyai Mathematica, 61(2), 147–153. Retrieved from https://studia.reviste.ubbcluj.ro/index.php/subbmathematica/article/view/5542

Issue

Section

Articles

Similar Articles

<< < 3 4 5 6 7 8 9 10 11 12 > >> 

You may also start an advanced similarity search for this article.