scholarly journals Fekete-Szegö Inequalities for Starlike Functions with respect to k-Symmetric Points of Complex Order

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
M. K. Aouf ◽  
R. M. El-Ashwah ◽  
S. M. El-Deeb
Keyword(s):  
Analytic Function ◽  
Fractional Derivatives ◽  
Starlike Functions ◽  
Upper Bounds ◽  
Complex Order ◽  
Symmetric Points

Sharp upper bounds of a3-μa22 for the function fz=z+∑m=2∞amzm belonging to certain subclass of starlike functions with respect to k-symmetric points of complex order are obtained. Also, applications of our results to certain functions defined through convolution with a normalized analytic function are given. In particular, Fekete-Szegö inequalities for certain classes of functions defined through fractional derivatives are obtained.

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.

scholarly journals On the Fekete-Szegö problem

2000 ◽  
Vol 24 (9) ◽  
pp. 577-581 ◽  
Author(s):  
B. A. Frasin ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Upper Bound ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Strongly Starlike Functions ◽  
Strongly Starlike

Letf(z)=z+a2z2+a3z3+⋯be an analytic function in the open unit disk. A sharp upper bound is obtained for|a3−μa22|by using the classes of strongly starlike functions of orderβand typeαwhenμ≥1.

scholarly journals Hankel determinant for a class of analytic functions of complex order defined by convolution

2015 ◽  
Vol 69 (2) ◽  
pp. 47
Author(s):  
S. M. El-Deeb ◽  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Complex Order ◽  
Second Hankel Determinant

In this paper, we obtain the Fekete-Szego inequalities for the functions of complex order defined by convolution. Also, we find upper bounds for the second Hankel determinant \(|a_2a_4-a_3^2|\) for functions belonging to the class \(S_{\gamma}^b(g(z);A,B)\).

scholarly journals Third Hankel determinant and Zalcman functional for a class of starlike functions with respect to symmetric points related with sine function

2021 ◽  
Vol 25 (01) ◽  
pp. 29-36
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Gangadharan Murugusundaramoorthy ◽  
Wali Khan Mashwani ◽  
Sibel Yalçin ◽  
...  
Keyword(s):  
Starlike Functions ◽  
Sine Function ◽  
Hankel Determinant ◽  
Symmetric Points

Coefficient bounds for a subclass of starlike functions of complex order

2011 ◽  
Vol 218 (3) ◽  
pp. 693-698
Author(s):  
Murat Çağlar ◽  
Erhan Deniz ◽  
Halit Orhan
Keyword(s):  
Starlike Functions ◽  
Coefficient Bounds ◽  
Complex Order

scholarly journals Some applications of a differential subordination

1999 ◽  
Vol 22 (3) ◽  
pp. 649-654 ◽  
Author(s):  
Yong Chan Kim ◽  
H. M. Srivastava
Keyword(s):  
Analytic Function ◽  
Integral Operator ◽  
Starlike Functions ◽  
Differential Subordination

A number of interesting criteria were given by earlier workers for a normalized analytic function to be in the familiar class𝔖*of starlike functions. The main object of the present paper is to extend and improve each of these earlier results. An application associated with an integral operator𝔉c(c>−1)is also considered.

scholarly journals Complex order fractional derivatives in viscoelasticity

2016 ◽  
Vol 20 (2) ◽  
pp. 175-195 ◽  
Author(s):  
Teodor M. Atanacković ◽  
Sanja Konjik ◽  
Stevan Pilipović ◽  
Dušan Zorica
Keyword(s):  
Fractional Derivatives ◽  
Complex Order

scholarly journals Research on Geometric Mappings in Complex Systems Analysis

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Yanyan Cui ◽  
Chaojun Wang ◽  
Sifeng Zhu
Keyword(s):  
Banach Spaces ◽  
Systems Analysis ◽  
Starlike Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Coefficient Estimates ◽  
Positive Real ◽  
Reinhardt Domains ◽  
Complex Order ◽  
Starlike Mappings

We mainly discuss the properties of a new subclass of starlike functions, namely, almost starlike functions of complex order λ, in one and several complex variables. We get the growth and distortion results for almost starlike functions of complex order λ. By the properties of functions with positive real parts and considering the zero of order k, we obtain the coefficient estimates for almost starlike functions of complex order λ on D. We also discuss the invariance of almost starlike mappings of complex order λ on Reinhardt domains and on the unit ball B in complex Banach spaces. The conclusions contain and generalize some known results.

scholarly journals Harmonic Starlike Functions with Respect to Symmetric Points

Axioms ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 3 ◽  
Author(s):  
Nak Eun Cho ◽  
Jacek Dziok
Keyword(s):  
Integral Representation ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Distortion Theorems ◽  
Harmonic Starlike ◽  
Symmetric Points

In the paper we define classes of harmonic starlike functions with respect to symmetric points and obtain some analytic conditions for these classes of functions. Some results connected to subordination properties, coefficient estimates, integral representation, and distortion theorems are also obtained.

Uniformly harmonic starlike functions of complex order

2017 ◽  
Vol 5 ◽  
pp. 67-74
Author(s):  
Syed Zakar Hussain Bukhari ◽  
Malik Ali Raza ◽  
Bushra Malik
Keyword(s):  
Starlike Functions ◽  
Complex Order ◽  
Harmonic Starlike
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