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Certain nth Order Differential Inequalities in the Complex Plane

Published online by Cambridge University Press:  20 November 2018

H. S. Al-Amiri
H. S. Al-Amiri*
Affiliation:
Department of Mathematics, Bowling Green State University, Bowling Green, OHIO 43403
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Abstract

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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 3 , 01 September 1978 , pp. 273 - 277
Copyright
Copyright © Canadian Mathematical Society 1978

References

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