scholarly journals The Generalized Janowski Starlike and Close-to-Starlike Log-Harmonic Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Maisarah Haji Mohd ◽  
Maslina Darus
Keyword(s):  
Unit Disc ◽  
Harmonic Mapping ◽  
Starlike Functions ◽  
Starlike Function ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disc

Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form defined on the open unit disc . The functions are in the class of the generalized Janowski starlike log-harmonic mapping, , with the functional in the class of the generalized Janowski starlike functions, . By means of these functions, we obtained results on the generalized Janowski close-to-starlike log-harmonic mappings, .

Radius of Limaçon starlikeness for Janowski starlike functions

2021 ◽  
Author(s):  
R. Kanaga ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Unit Disc ◽  
Starlike Functions ◽  
Starlike Function ◽  
Open Unit ◽  
Open Unit Disc ◽  
Class Of Functions

Let [Formula: see text] be an analytic function defined on the open unit disc [Formula: see text], with [Formula: see text], satisfying the subordination [Formula: see text], where [Formula: see text]. The domain [Formula: see text] is bounded by a Limaçon and the function [Formula: see text] is called starlike function associated with Limaçon domain. For [Formula: see text], we find the smallest disc [Formula: see text] and the largest disc [Formula: see text], centered at [Formula: see text] such that the domain [Formula: see text] is contained in [Formula: see text] and contains [Formula: see text]. By using this result, we find the radius of Limaçon starlikeness for the class of starlike functions of order [Formula: see text] [Formula: see text] and the class of functions [Formula: see text] satisfying [Formula: see text], [Formula: see text]. We give extension of our results for Janowski starlike functions.

scholarly journals Second Hankel Determinants for Some Subclasses of Biunivalent Functions Associated with Pseudo-Starlike Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
K. Rajya Laxmi ◽  
R. Bharavi Sharma
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Starlike Function ◽  
Open Unit ◽  
Hankel Determinant ◽  
Open Unit Disc ◽  
Hankel Determinants ◽  
Second Hankel Determinant ◽  
Starlike Univalent Function

We introduce second Hankel determinant of biunivalent analytic functions associated with λ-pseudo-starlike function in the open unit disc Δ subordinate to a starlike univalent function whose range is symmetric with respect to the real axis.

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 On Certain Subclass of Harmonic Starlike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Y. Lashin
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
New Class ◽  
Distortion Bounds ◽  
Harmonic Starlike

Coefficient conditions, distortion bounds, extreme points, convolution, convex combinations, and neighborhoods for a new class of harmonic univalent functions in the open unit disc are investigated. Further, a class preserving integral operator and connections with various previously known results are briefly discussed.

scholarly journals A CONVOLUTION APPROACH TO CERTAIN SUBCLASSES OF STARLIKE FUNCTIONS

1992 ◽  
Vol 23 (4) ◽  
pp. 311-320
Author(s):  
T . RAM REDDY ◽  
O. P. JUNEJA ◽  
K. SATHYANARAYANA
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Integral Transforms ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disc ◽  
Containment Property ◽  
Convolution Approach

The class $R_\gamma(A,B)$ for $-1\le B < A\le 1$ and $\gamma> (A- 1)/(1- B)$ consisting of normalised analytic functions in the open unit disc is defined with the help of Convolution technique. It consists of univalent starlike functions for $\gamma\ge 0$. We establish containment property, integral transforms and a sufficient condition for an analytic function to be in $R\gamma(A,B)$. Using the concept of dual spaces we find a convolution condition for a function in this class.

scholarly journals Some uniformly starlike functions with varying arguments

2004 ◽  
Vol 35 (1) ◽  
pp. 23-28 ◽  
Author(s):  
K. Vijaya ◽  
G. Murugusundaramoorthy
Keyword(s):  
Unit Disc ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Bound ◽  
Uniformly Starlike Functions ◽  
Uniformly Starlike ◽  
Varying Arguments

In this paper two new subclasses of starlike functions that are analytic and normalized in the open unit disc with varying arguments is introduced. For functions in these classes we obtained coefficient bound, distortion results and the extreme points.

scholarly journals Some new harmonic mappings convex in one direction and their convolution

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6131-6139
Author(s):  
Chinu Singla ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Unit Disc ◽  
Sufficient Conditions ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disc ◽  
Hadamard Products ◽  
New Family ◽  
Convex In One Direction ◽  
A New Technique ◽  
Necessary And Sufficient

In the present article, we construct a new family of locally univalent and sense preserving harmonic mappings by considering a suitable transformation of normalized univalent analytic functions defined in the open unit disc D. We present necessary and sufficient conditions for the functions of this new family to be univalent. Apart from studying properties of this new family, results about the convolutions or Hadamard products of functions from this family with some suitable analytic or harmonic mappings are proved by introducing a new technique which can also be used to simplify the proofs of earlier known results on convolutions of harmonic mappings. The technique presented also enables us to generalize existing such results.

scholarly journals Radius Problems for Starlike Functions Associated with the Tan Hyperbolic Function

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Khalil Ullah ◽  
Saira Zainab ◽  
Muhammad Arif ◽  
Maslina Darus ◽  
Meshal Shutaywi
Keyword(s):  
Holomorphic Function ◽  
Convex Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Hyperbolic Function ◽  
Open Unit Disc ◽  
Starlike And Convex Functions ◽  
Radius Problems

The aim of this particular article is at studying a holomorphic function f defined on the open-unit disc D = z ∈ ℂ : z < 1 for which the below subordination relation holds z f ′ z / f z ≺ q 0 z = 1 + tan h z . The class of such functions is denoted by S tan h ∗ . The radius constants of such functions are estimated to conform to the classes of starlike and convex functions of order β and Janowski starlike functions, as well as the classes of starlike functions associated with some familiar functions.

scholarly journals Some properties for \(\alpha\)-starlike functions with respect to \(k\)-symmetric points of complex order

2017 ◽  
Vol 71 (1) ◽  
pp. 1 ◽  
Author(s):  
H. E. Darwish ◽  
A. Y. Lashin ◽  
S. M. Sowileh
Keyword(s):  
Integral Representation ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Complex Order ◽  
Inclusion Relations ◽  
Symmetric Points

In the present work, we introduce the subclass \(\mathcal{T}_{\gamma ,\alpha<br />}^{k}(\varphi )\), of starlike functions with respect to \(k\)-symmetric points of complex order \(\gamma\) (\(\gamma \neq 0\)) in the open unit disc \(\vartriangle\). Some interesting subordination criteria, inclusion relations and the integral representation for functions belonging to this class are provided. The results obtained generalize some known results, and some other new results are obtained.

Generalized q-starlike functions

2017 ◽  
Vol 54 (4) ◽  
pp. 509-522 ◽  
Author(s):  
Khalida Inayat Noor ◽  
Sadia Riaz
Keyword(s):  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Distortion Theorems ◽  
Bounded Radius Rotation ◽  
Radius Problem

In this paper, we introduce a new concept of q-bounded radius rotation and define the class R*m(q), m ≥ 2, q ∈ (0, 1). The class R*2(q) coincides with S*q which consists of q-starlike functions defined in the open unit disc. Distortion theorems, coefficient result and radius problem are studied. Relevant connections to various known results are pointed out.

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