The radius of starlikeness of certain analytic functions

1971 ◽  
Vol 122 (4) ◽  
pp. 351-354
Author(s):  
Michael R. Ziegler
Keyword(s):  
Analytic Functions ◽  
Radius Of Starlikeness

scholarly journals On Certain Subclasses of Analytic Functions Defined by Differential Subordination

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Hesam Mahzoon
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Radius Of Starlikeness ◽  
Covering Theorems ◽  
Coefficient Inequalities

We introduce and study certain subclasses of analytic functions which are defined by differential subordination. Coefficient inequalities, some properties of neighborhoods, distortion and covering theorems, radius of starlikeness, and convexity for these subclasses are given.

Some properties of the analytic functions with bounded radius rotation

2019 ◽  
Vol 28 (1) ◽  
pp. 85-90
Author(s):  
YASAR POLATOGLU ◽  
◽  
ASENA CETINKAYA ◽  
OYA MERT ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Coefficient Estimate ◽  
Open Unit Disc ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
Bounded Radius Rotation

In the present paper, we introduce a new subclass of normalized analytic starlike functions by using bounded radius rotation associated with q- analogues in the open unit disc \mathbb D. We investigate growth theorem, radius of starlikeness and coefficient estimate for the new subclass of starlike functions by using bounded radius rotation associated with q- analogues denoted by \mathcal{R}_k(q), where k\geq2, q\in(0,1).

scholarly journals Certain Inequalities of Multivalent Analytic Functions with Missing Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-3
Author(s):  
Yi-Ling Cang ◽  
Cai-Mei Yan
Keyword(s):  
Analytic Functions ◽  
Radius Of Starlikeness

The purpose of the present paper is to derive the radius of starlikeness for certain p-valent functions with missing coefficients. The results obtained here are sharp.

Linear Combinations of Univalent Functions with Complex Coefficients

1971 ◽  
Vol 23 (4) ◽  
pp. 712-717 ◽  
Author(s):  
Robert K. Stump
Keyword(s):  
Linear Combination ◽  
Convex Domain ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Linear Combinations ◽  
Radius Of Starlikeness ◽  
Complex Constant ◽  
Complex Functions ◽  
Image Position ◽  
Complex Coefficients

Let U be the class of all normalized analytic functionswhere z ∈ E = {z : |z| < 1} and ƒ is univalent in E. Let K denote the sub-class of U consisting of those members that map E onto a convex domain. MacGregor [2] showed that if ƒ1 ∈ K and ƒ2 ∈ K and if1then F ∉ K when λ is real and 0 < λ < 1, and the radius of univalency and starlikeness for F is .In this paper, we examine the expression (1) when ƒ1 ∈ K, ƒ2 ∈ K and λ is a complex constant and find the radius of starlikeness for such a linear combination of complex functions with complex coefficients.

scholarly journals Radius of starlikeness for some classes containing non-univalent functions

2021 ◽  
pp. 2250009
Author(s):  
Shalu Yadav ◽  
Kanika Sharma ◽  
V. Ravichandran
Keyword(s):  
Unit Disk ◽  
Half Plane ◽  
Univalent Function ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Radius Of Starlikeness ◽  
The Past ◽  
The Right ◽  
Starlike Univalent Function

A starlike univalent function [Formula: see text] is characterized by [Formula: see text]; several subclasses of starlike functions were studied in the past by restricting [Formula: see text] to take values in a region [Formula: see text] on the right-half plane, or, equivalently, by requiring [Formula: see text] to be subordinate to the corresponding mapping of the unit disk [Formula: see text] to the region [Formula: see text]. The mappings [Formula: see text], [Formula: see text], defined by [Formula: see text] and [Formula: see text] map the unit disk [Formula: see text] to certain nice regions in the right-half plane. For normalized analytic functions [Formula: see text] with [Formula: see text] and [Formula: see text] are subordinate to the function [Formula: see text] for some analytic functions [Formula: see text] and [Formula: see text], we determine the sharp radius for them to belong to various subclasses of starlike functions.

scholarly journals Certain Properties of a Class of Functions Defined by Means of a Generalized Differential Operator

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 174
Author(s):  
Matthew Olanrewaju Oluwayemi ◽  
Kaliappan Vijaya ◽  
Adriana Cătaş
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Closure Properties ◽  
Integral Means ◽  
Radius Of Starlikeness ◽  
Generalized Differential ◽  
The Relationship ◽  
Class Of Functions

In this article, we construct a new subclass of analytic functions involving a generalized differential operator and investigate certain properties including the radius of starlikeness, closure properties and integral means result for the class of analytic functions with negative coefficients. Further, the relationship between the results and some known results in literature are also established.

scholarly journals On analytic functions with reference to an integral operator

1983 ◽  
Vol 28 (2) ◽  
pp. 207-215 ◽  
Author(s):  
R. Parvatham ◽  
T.N. Shanmugam
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Sharp Estimate ◽  
Radius Of Starlikeness ◽  
Image Position ◽  
Class Of Functions

Let E = {z: |z| < 1} and let H = {w : regular in E, w(0) = 0, |w(z)| < l, z ∈ E}.Let P(A, B) denote the class of functions in E which can be put in the form (1 + Aw(z))/(1 + Bw(z)), −1 ≤ A < B ≤ 1, w(z) ∈ H. Let S*(A, B) denote the class of functions f(z) of the form such that zf′(z)/f(z) ∈ P(A, B). If f(z) ∈ S*(A, B) and g(z) ∈ S*(C, D) then, in this paper the radius of starlikeness of order β (β ∈ [0, 1]) of the following integral operatoris determined. Conversely, a sharp estimate is obtained for the radius of starlikeness of the class of functionswhere g(z) and F(z) belong to the class S*(A, B).

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