Geodesic
Convolution conditions for bounded \(\alpha\)-starlike functions of complex order
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 1.

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

Let A be the class of analytic functions in the unit disc U of the complex plane ℂ with the normalization f(0)=f^^'(0)-1=0. We introduce a subclass S_M^∗(α ,b) of A, which unifies the classes of bounded starlike and convex functions of complex order. Making use of Salagean operator, a more general class S_M^∗(n,α ,b) (n≥ 0) related to S_M^∗(α ,b) is also considered under the same conditions. Among other things, we find convolution conditions for a function f∈ A to belong to the class S_M^∗(α ,b). Several properties of the class S_M^∗(n,α ,b) are investigated.
Keywords: Univalent functions, bounded starlike functions of complex order, bounded convex functions of complex order, \(\alpha\)-starlike functions 
@article{AUM_2017_71_1_a2,
     author = {Lashin, A. Y.},
     title = {Convolution conditions for bounded \(\alpha\)-starlike functions of complex order},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica },
     publisher = {mathdoc},
     volume = {71},
     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2017_71_1_a2/}
}
TY  - JOUR
AU  - Lashin, A. Y.
TI  - Convolution conditions for bounded \(\alpha\)-starlike functions of complex order
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
PY  - 2017
VL  - 71
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2017_71_1_a2/
LA  - en
ID  - AUM_2017_71_1_a2
ER  - 
%0 Journal Article
%A Lashin, A. Y.
%T Convolution conditions for bounded \(\alpha\)-starlike functions of complex order
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
%D 2017
%V 71
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2017_71_1_a2/
%G en
%F AUM_2017_71_1_a2
Lashin, A. Y. Convolution conditions for bounded \(\alpha\)-starlike functions of complex order. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 1. http://geodesic.mathdoc.fr/item/AUM_2017_71_1_a2/

[1] Aouf, M. K., Darwish, H. E., Attiya, A. A., On a class of certain analytic functions of complex order, Indian J. Pure Appl. Math. 32 (10) (2001), 1443-1452.

[2] El-Ashwah, R. M., Some convolution and inclusion properties for subclasses of bounded univalent functions of complex order, Thai J. Math. 12 (2) (2014), 373-384.

[3] Goodman, A. W., Univalent Functions, Vol. I, II, Tampa, Florida, 1983.

[4] Kulshrestha, P. K., Bounded Robertson functions, Rend. Mat. 6 (1) (1976), 137-150.

[5] Kulshrestha, P. K., Distortion of spiral-like mapping, Proc. Royal Irish Acad. 73A (1973) 1-5.

[6] Libera, R. J., Univalent \(\lambda\)-spiral functions, Canad. J. Mat. 19 (1967) 449-456.

[7] Nasr, M. A., Aouf, M. K., On convex functions of complex order, Mansoura Sci. Bull. 9 (1982), 565-582.

[8] Nasr, M. A., Aouf, M. K., Bounded convex functions of complex order, Mansoura Sci. Bull. 10 (1983), 513-526.

[9] Nasr, M. A., Aouf, M. K., Bounded starlike functions of complex order, Proc. Indian Acad. Sci. (Math. Sci.) 92 (2) (1983) 97-102.

[10] Nasr, M. A., Aouf, M. K., Starlike functions of complex order, J. Natur. Sci. Math. 25 (1985), 1-12.

[11] Padmanabhan, K. S., Ganesan, M. S., Convolution conditions for certain class of analytic functions, Indian J. Pure Appl. Math. 15 (1984), 777-780.

[12] Robertson, M. S., On the theory of univalent functions, Ann. of Math. 37 (1936), 374-408.

[13] Salagean, G. S., Subclasses of univalent functions, in: Complex Analysis – Fifth Romanian-Finnish Seminar (C. A. Cazacu, N. Boboc, M. Jurchescu, I. Suciu, eds.) Springer, Berlin–Heidelberg, 1983, 362-372.

[14] Silverman, H., Silvia, E. M., Telage, D., Convolution conditions for convexity and starlikeness and spiral-likeness, Math. Z. 162 (1978), 125-130.

[15] Sizuk, P. I., Regular functions \(f(z)\) for which \(zf'(z)\) is \(\lambda\)-spirallike, Proc. Amer. Math. Soc. 49 (1975), 151-160.

[16] Singh, R., Singh, V., On a class of bounded starlike functions, Indian J. Pure Appl. Math. 5 (8) (1974), 733-754.

[17] Wiatrowski, P., The coefficient of a certain family of holomorphic functions, Zeszyty Nauk. Uniw. Łódz. Nauki Mat. Przyrod. Ser. II No. 39 Mat. (1971), 75-85.