scholarly journals A Subclass of Harmonic Univalent Functions Defined by Salagean Integro Differential Operator

2020 ◽  
Vol 25 (3) ◽  
pp. 62-70
Author(s):  
Hasan Bayram
Keyword(s):  
Differential Operator ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Distortion Bounds ◽  
Coefficient Inequalities

In this paper, we scrutinize some fundamental features of a subclass of harmonic functions defined by a new operator. Like coefficient inequalities, convex combinations, distortion bounds.

Coefficient inequalities for new subclasses of bi-univalent functions defined by using the function fδ

2021 ◽  
Author(s):  
Fatma Sağsöz ◽  
Halit Orhan
Keyword(s):  
Differential Operator ◽  
Univalent Functions ◽  
Function Classes ◽  
Coefficient Inequalities

In this investigation, we introduce and study two new subclasses of bi-univalent functions defined by using the function [Formula: see text] and Salagean differential operator. Furthermore, we find estimates on the coefficients [Formula: see text] and [Formula: see text] for these function classes.

scholarly journals A Brief Study of Certain Class of Harmonic Functions of Bazilevič Type

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
A. T. Oladipo ◽  
D. Breaz
Keyword(s):  
Linear Operator ◽  
Harmonic Functions ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds

We define and investigate a new subclass of Bazilevič type harmonic univalent functions using a linear operator. We investigated the harmonic structures in terms of its coefficient conditions, extreme points, distortion bounds, convolution, and convex combination. So, also, we discussed the subordination properties for the functions in this class.

scholarly journals On (p,q)-Starlike Harmonic Functions Defined By Subordination

2021 ◽  
Vol 26 (4) ◽  
pp. 491-500
Author(s):  
Hasan BAYRAM ◽  
Sibel Yalçın
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds ◽  
Necessary And Sufficient

We introduce and investigate classes of (p,q)-starlike harmonic univalent functions defined by subordination. We first obtained a coefficient characterization of these functions. We give necessary and sufficient convolution conditions, distortion bounds, compactness and extreme points for the (p,q)-starlike harmonic univalent with negative coefficients.

scholarly journals Subclass of Harmonic Univalent Functions Associated with the Generalized Mittag-Leffler Type Functions

2020 ◽  
pp. 139-153
Author(s):  
Adnan Ghazy Alamoush
Keyword(s):  
Unit Disc ◽  
Harmonic Functions ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds

In the present paper, we introduce a new subclass of harmonic functions in the unit disc U defined by using the generalized Mittag-Leffler type functions. Coefficient conditions, extreme points, distortion bounds, convex combination are studied.

scholarly journals Subclasses of harmonic univalent functions associated with generalized Ruscheweyh operator

2019 ◽  
Vol 106 (120) ◽  
pp. 19-28
Author(s):  
Jacek Dziok ◽  
Sibel Yalçın ◽  
Şahsene Altınkaya
Keyword(s):  
Differential Operator ◽  
Univalent Functions ◽  
Extreme Points ◽  
Coefficient Bounds ◽  
Distortion Bounds ◽  
Necessary And Sufficient

We introduce a new subclass of functions defined by multiplier differential operator and give coefficient bounds for these subclasses. Also, we obtain necessary and sufficient convolution conditions, distortion bounds and extreme points for these subclasses of functions.

scholarly journals On Harmonic Functions Defined by Differential Operator with Respect tok-Symmetric Points

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Afaf A. Ali Abubaker ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Representation Theorem ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Distortion Theorem ◽  
Coefficient Condition ◽  
Symmetric Points

We introduce new classesMHkσ,s(λ,δ,α)andM¯Hkσ,s(λ,δ,α)of harmonic univalent functions with respect tok-symmetric points defined by differential operator. We determine a sufficient coefficient condition, representation theorem, and distortion theorem.

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 A New Subclass of Salagean-Type Harmonic Univalent Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Khalifa Al-Shaqsi ◽  
Maslina Darus ◽  
Olubunmi Abidemi Fadipe-Joseph
Keyword(s):  
Harmonic Functions ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Bounds

We define and investigate a new subclass of Salagean-type harmonic univalent functions. We obtain coefficient conditions, extreme points, distortion bounds, convolution, and convex combination for the above subclass of harmonic functions.

On certain subclasses of meromorphic univalent functions associated with a differential operator

2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Qazi Zahoor Ahmad ◽  
Khalida Inayat Noor ◽  
Janusz Sokół
Keyword(s):  
Differential Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Inequalities ◽  
Inclusion Results ◽  
Meromorphic Univalent Functions

AbstractIn this paper, we define new classes of meromorphic univalent functions defined in the punctured open unit disc by using a differential operator. Some inclusion results and coefficient inequalities for these classes are studied.

scholarly journals A subclass of harmonic univalent functions with positive coefficients

2010 ◽  
Vol 41 (3) ◽  
pp. 261-269 ◽  
Author(s):  
K. K. Dixit ◽  
Saurabh Porwal
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Distortion Bounds ◽  
Positive Coefficients ◽  
Complex Valued

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disc $U$ can be written in the form $f=h+\bar g$, where $h$ and $g$ are analytic in $U$. In this paper authors introduce the class, $R_H(\beta)$, $(1<\beta \le 2)$ consisting of harmonic univalent functions $f=h+\bar g$, where $h$ and $g$ are of the form $ h(z)=z+ \sum_{k=2}^\infty |a_k|z^k $ and $ g(z)= \sum_{k=1}^\infty |b_k| z^k $ for which $\Re\{h'(z)+g'(z)\}<\beta$. We obtain distortion bounds extreme points and radii of convexity for functions belonging to this class and discuss a class  preserving integral operator. We also show that class studied in this paper is closed under convolution and convex combinations.

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