Sufficient Conditions and Applications for Carathéodory Functions
Author
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-4, 4 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-01-30
Country of Publication
Egypt
No. of Pages
4
Main Subjects
Abstract EN
Let P be the class of functions of the form p(z)=1+∑n=1∞pnzn which are analytic in U.
By using the method of differential subordinations, we give some sufficient conditions for Carathéodory function, that is, if p(z)∈P satisfies p(z)≠0 (0<|z|<1) and p(z)m+λ(zp'(z)/(p(z))μ)≺h(z), where h(z)=((1+az)/(1+bz))m+λ(a-b)z/(1+bz)2-μ(1+az)μ, -1≤b0, m, μ∈{0,1,2}, m+μ≤2, then p(z)≺(1+az)/(1+bz).
Some useful consequences of this result are also given.
American Psychological Association (APA)
Xu, Neng. 2013. Sufficient Conditions and Applications for Carathéodory Functions. Journal of Mathematics،Vol. 2013, no. 2013, pp.1-4.
https://search.emarefa.net/detail/BIM-509045
Modern Language Association (MLA)
Xu, Neng. Sufficient Conditions and Applications for Carathéodory Functions. Journal of Mathematics No. 2013 (2013), pp.1-4.
https://search.emarefa.net/detail/BIM-509045
American Medical Association (AMA)
Xu, Neng. Sufficient Conditions and Applications for Carathéodory Functions. Journal of Mathematics. 2013. Vol. 2013, no. 2013, pp.1-4.
https://search.emarefa.net/detail/BIM-509045
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-509045