Geodesic
Certain nth Order Differential Inequalities in the Complex Plane
Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 273-277

Voir la notice de l'article provenant de la source Cambridge University Press

Let w(z) be regular in the unit disc U:|z|<l, with w(0) = 0 and let h(r, s, t) be a complex function defined in a domain D of C3. The author determines conditions on h such that if z∈U, then |w(z)|< 1 for z ∈ U and n= 0, 1, 2, .... Here Dnw(z) = (z/(l-z)n+1*w(z), where * stands for the Hadamard product (convolution). Some applications of the results to certain differential equations are given. 
Al-Amiri, H. S. Certain nth Order Differential Inequalities in the Complex Plane. Canadian mathematical bulletin, Tome 21 (1978) no. 3, pp. 273-277. doi: 10.4153/CMB-1978-048-9
@article{10_4153_CMB_1978_048_9,
     author = {Al-Amiri, H. S.},
     title = {Certain nth {Order} {Differential} {Inequalities} in the {Complex} {Plane}},
     journal = {Canadian mathematical bulletin},
     pages = {273--277},
     year = {1978},
     volume = {21},
     number = {3},
     doi = {10.4153/CMB-1978-048-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-048-9/}
}
TY  - JOUR
AU  - Al-Amiri, H. S.
TI  - Certain nth Order Differential Inequalities in the Complex Plane
JO  - Canadian mathematical bulletin
PY  - 1978
SP  - 273
EP  - 277
VL  - 21
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-048-9/
DO  - 10.4153/CMB-1978-048-9
ID  - 10_4153_CMB_1978_048_9
ER  - 
%0 Journal Article
%A Al-Amiri, H. S.
%T Certain nth Order Differential Inequalities in the Complex Plane
%J Canadian mathematical bulletin
%D 1978
%P 273-277
%V 21
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-048-9/
%R 10.4153/CMB-1978-048-9
%F 10_4153_CMB_1978_048_9

[1] 1. Jack, I. S., Functions starlike and convex of order a, J. London Math. Soc. (2) 3 (1971), 469-474. Google Scholar

[2] 2. Miller, S. S., A class of differential inequalities implying boundedness, III. J. of Math. 20 (1976), 647-649. Google Scholar

[3] 3. Miller, S. S. and Mocanu, P. T., Second order differential inequalities in the complex plane, to appear. Google Scholar

[4] 4. Ruscheweyh, S., New criteria for univalent functions, Proc. Amer. Math. Soc. vol. 49 (1975), 109-115. Google Scholar

Cité par Sources :