PRESERVING PROPERTIES OF THE GENERALIZED BERNARDI-LIBERA-LIVINGSTON INTEGRAL OPERATOR DEFINED ON SOME SUBCLASSES OF STARLIKE FUNCTIONS

Yıl 2017, Cilt: 5 Sayı: 2, 207 - 215, 15.10.2017

OLGA Engel ORSOLYA Agnes Pall-szabo

Öz

In this paper we study the properties of the image of some subclasses of starlike functions, through the generalized Bernardi - Libera - Livingston integral operator. A new subclass of functions with negative coefficients is introduced and we study some properties of this class.

Anahtar Kelimeler

Bernardi-Libera-Livingston integral operator, composition of functions, functions with negative coefficients, starlikeness

Kaynakça

• [1] O. Engel, On the composition of two starlike functions, Acta Univ. Apulensis, Vol:48 (2016), 47-53.
• [2] O. Engel, R. Szasz, Diferensiyel geometri, On a subclass of convex functions, Stud. Univ. Babeş - Bolyai Mathematica, Vol:59, No.2 (2016), 137-146.
• [3] S. S. Miller, P. T. Mocanu, Differential Subordinations Theory and Applications, Marcel Dekker, New York, Basel 2000.
• [4] P. T. Mocanu, T. Bulboaca, G. Şt. Salagean, Teoria Geometrica a Functiilor Univalente, Ed. a II-a, Casa Cartii de Stiinta, Cluj-Napoca, 2006, 460+9 pag., ISBN 973-686-959-8.
• [5] R. M. Ali, V. Ravichandran, N. Seenivasagan, Differential subordination and superordination of analytic functions dened by the multiplier transformation, Math. Inequal. Appl., Vol:12, No.1 (2009), 123-139.
• [6] N. Seenivasagan, R. M. Ali, V. Ravichandran, On Bernardi's integral operator and the Briot Bouquet differential subordination, J. of Math. Anal. and Appl., Vol:324 (2006), 663-668. MR2262499 (2007e:30026) Zbl 1104.30013 (SCI).
• [7] H. Silverman, A survey with open problems on univalent functions whose coefficients are negative, Rocky Montain J. Math., Vol:21 (1991), 1099-1125.