Koebe sets for certain classes of circularly symmetric functions
نویسندگان
چکیده
منابع مشابه
On Sandwich theorems for certain classes of analytic functions
The purpose of this present paper is to derive some subordination and superordination results for certain analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.
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Let D ⊂ C and 0 ∈ D. A set D is circularly symmetric if for each % ∈ R a set D ∩ {ζ ∈ C : |ζ| = %} is one of three forms: an empty set, a whole circle, a curve symmetric with respect to the real axis containing %. A function f ∈ A is circularly symmetric if f(∆) is a circularly symmetric set. The class of all such functions we denote by X. The above definitions were given by Jenkins in [2]. In ...
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For α ≥ 0, λ > 0, we consider theM α, λ b of normalized analytic α−λ convex functions defined in the open unit disc U. In this paper, we investigate the classM α, λ b, that is, Re{ zf ′ b z /fb z 1− α α 1 − λ zf ′ b z /fb z αλ 1 zf ′′ b z /f ′ b z } > 0, with fb is Koebe type, that is, fb z : z/ 1−zn . The subordination result for the aforementioned class will be given. Further, bymaking use of...
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1. In addition to the study devoted to the general class of normalized regular univalent functions in the unit circle considerable attention has been given to certain subclasses of these functions such as starlike functions, convex functions, and others. In view of the important role played by symmetrization methods in recent work it seems worth while to study a further subclass—the class of ci...
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2016
ISSN: 1631-073X
DOI: 10.1016/j.crma.2015.12.016