scholarly journals A Study of a Certain Family of Multivalent Functions Associated with Subordination

2021 ◽  
pp. 3009-3019
Author(s):  
Reem O. Rasheed ◽  
Kassim A. Jassim
Keyword(s):  
Coefficient Estimates ◽  
Growth Theorem ◽  
Radius Of Convexity

The aim of this paper is to introduce a certain family of new classes of multivalent functions associated with subordination. The various results obtained here for each of these classes include coefficient estimates radius of convexity, distortion and growth theorem.  

scholarly journals Applications of a New q -Difference Operator in Janowski-Type Meromorphic Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Bakhtiar Ahmad ◽  
Muhammad Ghaffar Khan ◽  
Mohamed Kamal Aouf ◽  
Wali Khan Mashwani ◽  
Zabidin Salleh ◽  
...  
Keyword(s):  
Differential Operator ◽  
Convex Functions ◽  
Difference Operator ◽  
Algebraic Property ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
Radius Of Convexity

The main aim of the present article is the introduction of a new differential operator in q -analogue for meromorphic multivalent functions which are analytic in punctured open unit disc. A subclass of meromorphic multivalent convex functions is defined using this new differential operator in q -analogue. Furthermore, we discuss a number of useful geometric properties for the functions belonging to this class such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity. Also, algebraic property of closure is discussed of functions belonging to this class. Integral representation problem is also proved for these functions.

scholarly journals Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1840
Author(s):  
Lei Shi ◽  
Bakhtiar Ahmad ◽  
Nazar Khan ◽  
Muhammad Ghaffar Khan ◽  
Serkan Araci ◽  
...  
Keyword(s):  
Differential Operator ◽  
Convex Functions ◽  
Starlike Functions ◽  
Distortion Theorem ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
New Class ◽  
Radius Of Convexity

By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex functions with the help of a q-differential operator. Furthermore, we investigate some useful properties such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity for this new subclass.

scholarly journals Some Geometric Properties for a Certain Class of Meromorphic Univalent Functions by Differential Operator

2021 ◽  
pp. 2667-2675
Author(s):  
Mohammed Hadi Lafta
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Growth Theorem ◽  
Closure Theorem ◽  
Major Target ◽  
Meromorphic Univalent Functions

The major target of this paper is to study a confirmed class of meromorphic univalent functions . We procure several results, such as those related to coefficient estimates, distortion and growth theorem, radii of starlikeness, and convexity for this class, n additionto hadamard product, convex combination, closure theorem, integral operators, and  neighborhoods.

scholarly journals Piggyback-Dualitäten

1985 ◽  
Vol 32 (1) ◽  
pp. 1-32 ◽  
Author(s):  
B.A. Davey ◽  
H. Werner
Keyword(s):  
Series Expansion ◽  
Analytic Functions ◽  
Laurent Series ◽  
Integral Operators ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Radius Of Convexity ◽  
Distortion Theorems ◽  
Convolution Properties

For the class of meromorphically starlike functions of prescribed order, the concept of type has been introduced. A characterization of meromorphically starlike functions of order α and type β has been obtained when the coefficients in its Laurent series expansion about the origin are all positive. This leads to a study of coefficient estimates, distortion theorems, radius of convexity estimates, integral operators, convolution properties et cetera for this class. It is seen that the class considered demonstrates, in some respects, properties analogous to those possessed by the corresponding class of univalent analytic functions with negative coefficients.

scholarly journals Properties of Functions Formed Using the Sakaguchi and Gao-Zhou Concept

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 310
Author(s):  
Jonathan Aaron Azlan Mosiun ◽  
Suzeini Abdul Halim
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
New Class ◽  
Radius Of Convexity

This paper introduces a new class related to close-to-convex functions denoted by K s k , N . This class is based on combining the concepts of starlike functions with respect to N-ply symmetry points of the order α , introduced by Chand and Singh; and K s ( k ) , introduced by Wang, Gao, and Yuan, which are generalizations of the classes of functions introduced by Sakaguchi and Gao and Zhou, respectively. We investigate the class for several properties including coefficient estimates, distortion and growth theorems, and the radius of convexity.

New subfamily of meromorphic multivalent starlike functions in circular domain involving q-differential operator

2018 ◽  
Vol 68 (5) ◽  
pp. 1049-1056 ◽  
Author(s):  
Muhammed Arif ◽  
Bakhtiar Ahmad
Keyword(s):  
Differential Operator ◽  
Linear Differential Operator ◽  
Starlike Functions ◽  
Circular Domain ◽  
Coefficient Estimates ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Linear Differential

Abstract The main object of the present paper is to investigate a number of useful properties such as sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikness and radius of convexity for a new subclass of meromorphic multivalent starlike functions, which are defined here by means of a newly defined q-linear differential operator.

scholarly journals Meromorphic univalent functions with positive coefficients

1985 ◽  
Vol 32 (2) ◽  
pp. 161-176 ◽  
Author(s):  
M.L. Mogra ◽  
T.R. Reddy ◽  
O.P. Juneja
Keyword(s):  
Univalent Functions ◽  
Integral Operators ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Radius Of Convexity ◽  
Distortion Theorems ◽  
Convolution Properties ◽  
Positive Coefficients ◽  
Meromorphic Univalent Functions

For the class of meromorphically starlike functions of prescribed order, the concept of type has been introduced. A characterization of meromorphically starlike functions of order α and type β has been obtained when the coefficients in its Laurent series expansion about the origin are all positive. This leads to a study of coefficient estimates, distortion theorems, radius of convexity estimates, integral operators, convolution properties et cetera for this class. It is seen that the class considered demonstrates, in some respects, properties analogous to those possessed by the corresponding class of univalent analytic functions with negative coefficients.

scholarly journals Applications of Some Generalized Janowski Meromorphic Multivalent Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Bakhtiar Ahmad ◽  
Muhammad Ghaffar Khan ◽  
Maslina Darus ◽  
Wali Khan Mashwani ◽  
Muhammad Arif
Keyword(s):  
Convex Combination ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
Growth Theorem ◽  
Quantum Calculus ◽  
Class Of Functions

In this article, the ideas of post-quantum calculus and meromorphic multivalent functions are combined and some applications of these functions are discussed. We introduce a new subclass of meromorphic multivalent functions in association with Janowski domain. We investigate and study some useful geometric properties of this class of functions such as sufficiency criteria, distortion problem, growth theorem, radii of starlikeness and convexity, convex combination, and coefficient estimates for this class.

scholarly journals A class of strongly close-to-convex functions

2019 ◽  
Vol 38 (6) ◽  
pp. 9-24
Author(s):  
R. K. Raina ◽  
Poonam Sharma ◽  
Janusz Sokol
Keyword(s):  
Integral Operator ◽  
Convex Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Coefficient Estimates ◽  
Special Cases ◽  
Radius Of Convexity

In this paper, we study a class of strongly close-to-convex functions $f(z)$ analytic in the unit disk $\mathbb{U}$ with $f(0)=0,f^{\prime }(0)=1$ satisfying for some convex function $g(z)$ the condition that\begin{equation*}\frac{zf^{\prime }(z)}{g(z)}\prec \left( \frac{1+Az}{1+Bz}\right) ^{m}\end{equation*}%\begin{equation*}\left( -1\leq A\leq 1,-1\leq B\leq 1\ \left( A\neq B\right) ,0<m\leq 1;z\in\mathbb{U}\right) .\end{equation*}%We obtain for functions belonging to this class, the coefficient estimates, bounds, certain results based on an integral operator and radius of convexity. We also deduce a number of useful special cases and consequences of the various results which are presented in this paper.

scholarly journals A Class of Analytic Functions with Missing Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Ding-Gong Yang ◽  
Jin-Lin Liu
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Sharp Bounds ◽  
Radius Of Convexity ◽  
Convolution Properties ◽  
Class Of Functions

Let and denote the class of functions of the form which are analytic in the open unit disk and satisfy the following subordination condition , for, for. We obtain sharp bounds on , and coefficient estimates for functions belonging to the class . Conditions for univalency and starlikeness, convolution properties, and the radius of convexity are also considered.

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