scholarly journals Coefficient Estimate Problem for a New Subclass of Biunivalent Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
N. Magesh ◽  
T. Rosy ◽  
S. Varma
Keyword(s):  
Unit Disc ◽  
Function Class ◽  
Open Unit ◽  
Coefficient Estimate ◽  
Open Unit Disc ◽  
Estimate Problem

We introduce a unified subclass of the function class Σ of biunivalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients |a2| and |a3| for functions in this subclass. In addition, many relevant connections with known or new results are pointed out.

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 Coefficients assessment for certain subclasses of bi-univalent functions related with quasi-subordination

2020 ◽  
Vol 108 (122) ◽  
pp. 155-162
Author(s):  
Sibel Yalçın ◽  
Waggas Atshan ◽  
Haneen Hassan
Keyword(s):  
Univalent Function ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disc

We investigate specific new subclasses of the function class ? of bi-univalent function defined in the open unit disc, which is connected with quasi-subordination. We find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in these subclasses. Already pointed out are some documented and new implications of those findings.

scholarly journals Subclasses of Bi-Univalent Functions Defined by Frasin Differential Operator

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 783 ◽  
Author(s):  
Ibtisam Aldawish ◽  
Tariq Al-Hawary ◽  
B. A. Frasin
Keyword(s):  
Analytic Function ◽  
Differential Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Open Unit Disc ◽  
Class A ◽  
Class Of Functions

Let Ω denote the class of functions f ( z ) = z + a 2 z 2 + a 3 z 3 + ⋯ belonging to the normalized analytic function class A in the open unit disk U = z : z < 1 , which are bi-univalent in U , that is, both the function f and its inverse f − 1 are univalent in U . In this paper, we introduce and investigate two new subclasses of the function class Ω of bi-univalent functions defined in the open unit disc U , which are associated with a new differential operator of analytic functions involving binomial series. Furthermore, we find estimates on the Taylor–Maclaurin coefficients | a 2 | and | a 3 | for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

scholarly journals Maclaurin Coefficient Estimates of Bi-Univalent Functions Connected with the q-Derivative

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 418 ◽  
Author(s):  
Sheza M. El-Deeb ◽  
Teodor Bulboacă ◽  
Bassant M. El-Matary
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper we introduce a new subclass of the bi-univalent functions defined in the open unit disc and connected with a q-analogue derivative. We find estimates for the first two Taylor-Maclaurin coefficients a 2 and a 3 for functions in this subclass, and we obtain an estimation for the Fekete-Szegő problem for this function class.

scholarly journals Coefficient Bounds for Certain Subclasses of Bi-Univalent Function

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
N. Magesh ◽  
V. Prameela
Keyword(s):  
Univalent Function ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Bounds

We introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients|a2|and|a3|for functions in these new subclasses. Also consequences of the results are pointed out.

scholarly journals Coefficient estimate for a subclass of close-to-convex functionswith respect to symmetric points

2011 ◽  
Vol 42 (2) ◽  
pp. 217-222
Author(s):  
B. S. Mehrok ◽  
Gagandeep Singh ◽  
Deepak Gupta
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Coefficient Estimate ◽  
Open Unit Disc ◽  
Symmetric Points

For reals $A,B,C,D$  such that  $-1\le D \le  B< A\le  C\le 1$, a subclass $K_s(A,B;C,D)$ of analytic functions $f(z)=z+\sum_{k=2}^\infty a_kz^k $ in the open unit disc $E=\{z:|z|<1\} $ is introduced. The object of the present paper is todetermine the coefficient estimate for functions $f(z)$ belonging tothe class  $K_s(A,B;C,D)$.

scholarly journals Maclaurin Coefficient Estimates for New Subclasses of Bi-univalent Functions Connected with a q-Analogue of Bessel Function

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Sheza M. El-Deeb
Keyword(s):  
Bessel Function ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper, we introduce new subclasses of the function class Σ of bi-univalent functions connected with a q-analogue of Bessel function and defined in the open unit disc. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients a2 and a3 for functions in these new subclasses.

An argument of a function in H1/2

2012 ◽  
Vol 55 (2) ◽  
pp. 507-511
Author(s):  
Takahiko Nakazi ◽  
Takanori Yamamoto
Keyword(s):  
Hardy Space ◽  
Simple Proof ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc

AbstractLet H1/2 be the Hardy space on the open unit disc. For two non-zero functions f and g in H1/2, we study the relation between f and g when f/g ≥ 0 a.e. on ∂D. Then we generalize a theorem of Neuwirth and Newman and Helson and Sarason with a simple proof.

scholarly journals Harmonic univalent functions defined by post quantum calculus operators

2019 ◽  
Vol 11 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Om P. Ahuja ◽  
Asena Çetinkaya ◽  
V. Ravichandran
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Quantum Calculus ◽  
Special Cases ◽  
The Family ◽  
Covering Theorems

Abstract We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.

Approximation by Unimodular Functions

1971 ◽  
Vol 23 (2) ◽  
pp. 257-269 ◽  
Author(s):  
Stephen Fisher
Keyword(s):  
Blaschke Product ◽  
Uniform Approximation ◽  
Unit Disc ◽  
Open Unit ◽  
Blaschke Products ◽  
Open Unit Disc ◽  
Pointwise Approximation ◽  
Finite Blaschke Product ◽  
Image Position ◽  
Restricted Zeros

The theorems in this paper are all concerned with either pointwise or uniform approximation by functions which have unit modulus or by convex combinations of such functions. The results are related to, and are outgrowths of, the theorems in [4; 5; 10].In § 1, we show that a function bounded by 1, which is analytic in the open unit disc Δ and continuous on may be approximated uniformly on the set where it has modulus 1 (subject to certain restrictions; see Theorem 1) by a finite Blaschke product; that is, by a function of the form*where |λ| = 1 and |αi| < 1, i = 1, …, N. In § 1 we also discuss pointwise approximation by Blaschke products with restricted zeros.

Sign in / Sign up

Export Citation Format

Share Document