scholarly journals Some Classes of Harmonic Mapping with a Symmetric Conjecture Point Defined by Subordination

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 548
Author(s):  
Lina Ma ◽  
Shuhai Li ◽  
Xiaomeng Niu
Keyword(s):  
Harmonic Function ◽  
Univalent Functions ◽  
Harmonic Mapping ◽  
Conjugate Points ◽  
Original Research ◽  
Coefficient Estimates ◽  
Covering Theorem ◽  
Geometric Properties ◽  
Distortion Estimates ◽  
First Time

In the paper, we introduce some subclasses of harmonic mapping, the analytic part of which is related to general starlike (or convex) functions with a symmetric conjecture point defined by subordination. Using the conditions satisfied by the analytic part, we obtain the integral expressions, the coefficient estimates, distortion estimates and the growth estimates of the co-analytic part g, and Jacobian estimates, the growth estimates and covering theorem of the harmonic function f. Through the above research, the geometric properties of the classes are obtained. In particular, we draw figures of extremum functions to better reflect the geometric properties of the classes. For the first time, we introduce and obtain the properties of harmonic univalent functions with respect to symmetric conjugate points. The conclusion of this paper extends the original research.

Starlike and convex functions with respect to symmetric conjugate points involving conical domain

2018 ◽  
Vol 68 (1) ◽  
pp. 89-102
Author(s):  
C. Ramachandran ◽  
R. Ambrose Prabhu ◽  
Srikandan Sivasubramanian
Keyword(s):  
Convex Functions ◽  
Domain Growth ◽  
Conjugate Points ◽  
Coefficient Estimates ◽  
Interesting Application ◽  
New Class ◽  
Starlike And Convex Functions ◽  
Distortion Estimates ◽  
Symmetric Points

AbstractEnough attentions to domains related to conical sections has not been done so far although it deserves more. Making use of the conical domain the authors have defined a new class of starlike and Convex Functions with respect to symmetric points involving the conical domain. Growth and distortion estimates are studied with convolution using domains bounded by conic regions. Certain coefficient estimates are obtained for domains bounded by conical region. Finally interesting application of the results are also highlighted for the function Ωk,βdefined by Noor.

scholarly journals Coefficient Estimates for Bi-Univalent Functions in Connection with Symmetric Conjugate Points Related to Horadam Polynomial

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1888
Author(s):  
S. Melike Aydoğan ◽  
Zeliha Karahüseyin
Keyword(s):  
Univalent Functions ◽  
Conjugate Points ◽  
Coefficient Estimates ◽  
Open Disc ◽  
Coefficient Bounds ◽  
Special Cases

In the current study, we construct a new subclass of bi-univalent functions with respect to symmetric conjugate points in the open disc E, described by Horadam polynomials. For this subclass, initial Maclaurin coefficient bounds are acquired. The Fekete–Szegö problem of this subclass is also acquired. Further, some special cases of our results are designated.

scholarly journals On the Generalization of a Class of Harmonic Univalent Functions Defined by Differential Operator

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 312
Author(s):  
Aqeel Ketab AL-khafaji ◽  
Waggas Galib Atshan ◽  
Salwa Salman Abed
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class

In this article, a new class of harmonic univalent functions, defined by the differential operator, is introduced. Some geometric properties, like, coefficient estimates, extreme points, convex combination and convolution (Hadamard product) are obtained.

scholarly journals A Class of Harmonic Univalent Functions Defined by Differential Operator and the Generalization

2020 ◽  
pp. 1440-1445
Author(s):  
Faten Fakher Aubdulnabi ◽  
Kassim A. Jassim
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class

In this paper, a new class of harmonic univalent functions was defined by the differential operator. We obtained some geometric properties, such as the coefficient estimates, convex combination, extreme points, and convolution (Hadamard product), which are required

scholarly journals A class of harmonic functions associated with a generalized differential operator

2020 ◽  
Vol 108 (122) ◽  
pp. 145-154
Author(s):  
Sarika Verma ◽  
Deepali Khurana ◽  
Raj Kumar
Keyword(s):  
Differential Operator ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class ◽  
Inclusion Relations ◽  
Generalized Differential

We introduce a new class of harmonic univalent functions by using a generalized differential operator and investigate some of its geometric properties, like, coefficient estimates, extreme points and inclusion relations. Finally, we show that this class is invariant under Bernandi-Libera-Livingston integral for harmonic functions.

scholarly journals Coefficient estimates for Bi-univalent functions with respect to symmetric conjugate points associated with Horadam Polynomials

2020 ◽  
Vol 8 (2) ◽  
pp. 565-569
Author(s):  
Jayaraman Sivapalan ◽  
Nanjundan Magesh ◽  
Samy Murthy
Keyword(s):  
Univalent Functions ◽  
Conjugate Points ◽  
Coefficient Estimates

Coefficient estimates for certain subclass of bi-univalent functions associated with the class Pm(b, β)

2018 ◽  
Author(s):  
Amit Soni ◽  
Kamal Kumar Mishra ◽  
Sanjay Issar
Keyword(s):  
Univalent Functions ◽  
Coefficient Estimates

Coefficient estimates for some subclasses of bi-univalent functions

2017 ◽  
Vol 5 ◽  
pp. 189-195
Author(s):  
Andy Liew Pik Hern ◽  
Aini Janteng
Keyword(s):  
Univalent Functions ◽  
Coefficient Estimates

Coefficient estimates for a certain class of analytic and bi-univalent functions defined by fractional derivative

2014 ◽  
Vol 352 (12) ◽  
pp. 1005-1010 ◽  
Author(s):  
Gülfem Akın ◽  
Sevtap Sümer Eker
Keyword(s):  
Fractional Derivative ◽  
Univalent Functions ◽  
Coefficient Estimates

scholarly journals Coefficient Estimates and the Fekete–Szegö Problem for New Classes of m-Fold Symmetric Bi-Univalent Functions

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 129
Author(s):  
Georgia Irina Oros ◽  
Luminiţa-Ioana Cotîrlă
Keyword(s):  
Univalent Functions ◽  
Coefficient Estimates ◽  
Quantum Calculus

The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor–Maclaurin coefficients |am+1| and |a2m+1| are obtained and, furthermore, the much investigated aspect of Fekete–Szegő functional is also considered for each of the new classes.

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