On subordination for classes of non-Bazilevic type
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 54 (2010) no. 2

Voir la notice de l'article provenant de la source Library of Science

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
@article{AUM_2010_54_2_a6,
     author = {Ibrahim, Rabha W. and Darus, Maslina and Tuneski, Nikola},
     title = {On subordination for classes of {non-Bazilevic} type},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica},
     publisher = {mathdoc},
     volume = {54},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2010_54_2_a6/}
}
TY  - JOUR
AU  - Ibrahim, Rabha W.
AU  - Darus, Maslina
AU  - Tuneski, Nikola
TI  - On subordination for classes of non-Bazilevic type
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica
PY  - 2010
VL  - 54
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2010_54_2_a6/
LA  - en
ID  - AUM_2010_54_2_a6
ER  - 
%0 Journal Article
%A Ibrahim, Rabha W.
%A Darus, Maslina
%A Tuneski, Nikola
%T On subordination for classes of non-Bazilevic type
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica
%D 2010
%V 54
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2010_54_2_a6/
%G en
%F AUM_2010_54_2_a6
Ibrahim, Rabha W.; Darus, Maslina; Tuneski, Nikola. On subordination for classes of non-Bazilevic type. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 54 (2010) no. 2. http://geodesic.mathdoc.fr/item/AUM_2010_54_2_a6/

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

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

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

[4] 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.

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

[6] 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.

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

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

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

[10] 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.

[11] 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.

[12] 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.

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

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

[15] 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.