On subordination for classes of non-Bazilevic type

Rabha W. Ibrahim, Maslina Darus, Nikola Tuneski

Abstract


We give some subordination results for new classes of normalized analytic functions containing differential operator of non-Bazilevic type in the open unit disk. By using Jack’s lemma, sufficient conditions for this type of operator are also discussed.

Keywords


Fractional calculus; subordination; non-Bazilevic function; Jack’s lemma

Full Text:

PDF

References


Darus, M., Ibrahim, R. W., Coefficient inequalities for a new class of univalent functions, Lobachevskii J. Math. 29(4) (2008), 221-229.

Ibrahim, R. W., Darus, M., On subordination theorems for new classes of normalize analytic functions, Appl. Math. Sci. (Ruse) 2(56) (2008), 2785-2794.

Ibrahim, R. W., Darus, M., Subordination for new classes of non-Bazilevic type, UNRI-UKM Symposium, KE-4 (2008).

Ibrahim, R. W., Darus, M., Differential subordination results for new classes of the family (mathcal{E}(Phi, Psi)), JIPAM. J. Ineq. Pure Appl. Math. 10(1) (2009), Art. 8, 9 pp.

Jack, I. S., Functions starlike and convex of order k, J. London Math. Soc. 3 (1971), 469-474 .

Miller, S. S., Mocanu, P. T., Differential Subordinantions. Theory and Applications, Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker, Inc., New York, 2000.

Miller, K. S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons, Inc., New York, 1993.

Obradovic, M., A class of univalent functions, Hokkaido Math. J. 27(2) (1998), 329-335.

Raina, R. K., On certain class of analytic functions and applications to fractional calculus operator, Integral Transform. Spec. Funct. 5 (1997), 247-260.

Raina, R. K., Srivastava, H. M., A certain subclass of analytic functions associated with operators of fractional calculus, Comput. Math. Appl. 32 (1996), 13-19.

Shanmugam, T. N., Ravichangran, V. and Sivasubramanian, S., Differential sandwich theorems for some subclasses of analytic functions, Austral. J. Math. Anal. Appl. 3(1) (2006), 1-11.

Srivastava, H. M., Owa, S. (Eds.), Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press, John Wiley and Sons, New York, Chichester, Brisbane, Toronto, 1989.

Srivastava, H. M., Owa, S. (Eds.), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London, Hong Kong, 1992.

Tuneski, N., Darus, M., Fekete-Szego functional for non-Bazilevic functions, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 18(2) (2002), 63-65.

Wang, Z., Gao, C. and Liao, M., On certain generalized class of non-Bazilevic functions, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 21(2) (2005), 147-154.




DOI: http://dx.doi.org/10.2478/v10062-010-0014-x
Date of publication: 2016-07-29 10:39:55
Date of submission: 2016-07-28 22:26:54


Statistics


Total abstract view - 1082
Downloads (from 2020-06-17) - PDF - 802

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2010 Rabha W. Ibrahim, Maslina Darus, Nikola Tuneski