![](/images/graphics-bg.png)
Differential Subordinations for Nonanalytic Functions
Joint Authors
Oros, Gheorghe
Oros, Georgia Irina
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-18
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
In the paper by Mocanu (1980), Mocanu has obtained sufficient conditions for a function in the classes C 1 ( U ) , respectively, and C 2 ( U ) to be univalent and to map U onto a domain which is starlike (with respect to origin), respectively, and convex.
Those conditions are similar to those in the analytic case.
In the paper by Mocanu (1981), Mocanu has obtained sufficient conditions of univalency for complex functions in the class C 1 which are also similar to those in the analytic case.
Having those papers as inspiration, we try to introduce the notion of subordination for nonanalytic functions of classes C 1 and C 2 following the classical theory of differential subordination for analytic functions introduced by Miller and Mocanu in their papers (1978 and 1981) and developed in their book (2000).
Let Ω be any set in the complex plane C , let p be a nonanalytic function in the unit disc U , p ∈ C 2 ( U ), and let ψ ( r , s , t ; z ) : C 3 × U → C .
In this paper, we consider the problem of determining properties of the function p , nonanalytic in the unit disc U , such that p satisfies the differential subordination ψ ( p ( z ) , D p ( z ) , D 2 p ( z ) - D p ( z ) ; z ) ⊂ Ω ⇒ p ( U ) ⊂ Δ .
American Psychological Association (APA)
Oros, Georgia Irina& Oros, Gheorghe. 2014. Differential Subordinations for Nonanalytic Functions. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1033633
Modern Language Association (MLA)
Oros, Georgia Irina& Oros, Gheorghe. Differential Subordinations for Nonanalytic Functions. Abstract and Applied Analysis No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-1033633
American Medical Association (AMA)
Oros, Georgia Irina& Oros, Gheorghe. Differential Subordinations for Nonanalytic Functions. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1033633
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033633