scholarly journals Fekete-Szegö Problems for Quasi-Subordination Classes

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Maisarah Haji Mohd ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk

An analytic functionfis quasi-subordinate to an analytic functiong, in the open unit disk if there exist analytic functionsφandw, with|φ(z)|≤1,w(0)=0and|w(z)|<1such thatf(z)=φ(z)g(w(z)). Certain subclasses of analytic univalent functions associated with quasi-subordination are defined and the bounds for the Fekete-Szegö coefficient functional|a3-μa22|for functions belonging to these subclasses are derived.

scholarly journals On a Length Problem for Univalent Functions

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 266 ◽  
Author(s):  
Mamoru Nunokawa ◽  
Janusz Sokół ◽  
Nak Cho
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk

Let g be an analytic function with the normalization in the open unit disk. Let L ( r ) be the length of g ( { z : | z | = r } ) . In this paper we present a correspondence between g and L ( r ) for the case when g is not necessary univalent. Furthermore, some other results related to the length of analytic functions are also discussed.

scholarly journals The order of convexity for an integral operator

2016 ◽  
Vol 32 (1) ◽  
pp. 123-129
Author(s):  
VIRGIL PESCAR ◽  
◽  
CONSTANTIN LUCIAN ALDEA ◽  
◽  
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Order Of Convexity

In this paper we consider an integral operator for analytic functions in the open unit disk and we derive the order of convexity for this integral operator, on certain classes of univalent functions.

Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
S. P. Goyal ◽  
Rakesh Kumar
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

AbstractIn the present paper, we obtain the estimates on initial coefficients of normalized analytic function f in the open unit disk with f and its inverse g = f

scholarly journals On the second hankel determinant for the kth-root transform of analytic functions

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 227-245 ◽  
Author(s):  
Najla Alarifi ◽  
Rosihan Ali ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
The Given ◽  
Logarithmically Convex Functions

Let f be a normalized analytic function in the open unit disk of the complex plane satisfying zf'(z)/f(z) is subordinate to a given analytic function ?. A sharp bound is obtained for the second Hankel determinant of the kth-root transform z[f(zk)/zk]1/k. Best bounds for the Hankel determinant are also derived for the kth-root transform of several other classes, which include the class of ?-convex functions and ?-logarithmically convex functions. These bounds are expressed in terms of the coefficients of the given function ?, and thus connect with earlier known results for particular choices of ?.

scholarly journals Generalizing Certain Analytic Functions Correlative to the n-th Coefficient of Certain Class of Bi-Univalent Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hameed Ur Rehman ◽  
Maslina Darus ◽  
Jamal Salah
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Positive Real Part ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Positive Real ◽  
Faber Polynomial ◽  
Coefficient Problems

In the present paper, the authors implement the two analytic functions with its positive real part in the open unit disk. New types of polynomials are introduced, and by using these polynomials with the Faber polynomial expansion, a formula is structured to solve certain coefficient problems. This formula is applied to a certain class of bi-univalent functions and solve the n -th term of its coefficient problems. In the last section of the article, several well-known classes are also extended to its n -th term.

scholarly journals Radius of Star-Likeness for Certain Subclasses of Analytic Functions

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2448
Author(s):  
Caihuan Zhang ◽  
Mirajul Haq ◽  
Nazar Khan ◽  
Muhammad Arif ◽  
Khurshid Ahmad ◽  
...  
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Inverse Function ◽  
Open Unit ◽  
Open Unit Disk ◽  
Sine Function ◽  
Exponential Functions ◽  
Lemniscate Of Bernoulli ◽  
Rotation Function

In this paper, we investigate a normalized analytic (symmetric under rotation) function, f, in an open unit disk that satisfies the condition ℜfzgz>0, for some analytic function, g, with ℜz+1−2nzgz>0,∀n∈N. We calculate the radius constants for different classes of analytic functions, including, for example, for the class of star-like functions connected with the exponential functions, i.e., the lemniscate of Bernoulli, the sine function, cardioid functions, the sine hyperbolic inverse function, the Nephroid function, cosine function and parabolic star-like functions. The results obtained are sharp.

scholarly journals On Sandwich Theorems Results for Certain Univalent Functions Defined by Generalized Operators

2021 ◽  
pp. 2376-2383
Author(s):  
Waggas Galib Atshan ◽  
Aqeel Ahmed Redha Ali
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Subordination And Superordination

In this present paper, we obtain some differential subordination and superordination results, by using generalized operators for certain subclass of analytic functions in the open unit disk. Also, we derive some sandwich results.

Estimates for the Koebe Constant and the Second Coefficient for Some Classes of Univalent Functions

1980 ◽  
Vol 32 (6) ◽  
pp. 1311-1324 ◽  
Author(s):  
D. Bshouty ◽  
W. Hengartner ◽  
G. Schober
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
The Other ◽  
Open Unit ◽  
Open Unit Disk ◽  
Identity Mapping ◽  
The Best Possible Constant

Let S be the set of all normalized univalent analytic functions ƒ(z) = z + a2z2 + … in the open unit disk U. Then ƒ(U) contains the disk . Here is the best possible constant and is referred to as the Koebe constant for S. On the other extreme, ƒ(U) cannot contain the disk {|w| < 1}; unless ƒ is the identity mapping.In order to interpolate between the class S and the identity mapping, one may introduce the families , of functions ƒ ∈ S such that ƒ(U) contains the disk {|w| < d};. Then S(d1) ⊃ S(d2) for d1 < d2, and S(1) contains only the identity mapping. It is obvious that d is the “Koebe constant” for S(d). The relation between d and the second coefficient a2 has been studied by E. Netanyahu [5, 6].

scholarly journals Initial Coefficients of Biunivalent Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
See Keong Lee ◽  
V. Ravichandran ◽  
Shamani Supramaniam
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Special Cases

An analytic functionfdefined on the open unit disk is biunivalent if the functionfand its inversef-1are univalent in𝔻. Estimates for the initial coefficients of biunivalent functionsfare investigated whenfandf-1, respectively, belong to some subclasses of univalent functions. Some earlier results are shown to be special cases of our results.

scholarly journals On Differential Sandwich Theorems of Meromorphic Univalent Functions

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Waggas Galib Atshan ◽  
Rajaa Ali Hiress
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Meromorphic Univalent Functions

        By using of linear  operator, we obtain some Subordinations  and superordinations results for certain normalized meromorphic univalent analytic functions in the in the punctured open unit disk   Also we derive some sandwich theorems .

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