scholarly journals A Study of Multivalent q-starlike Functions Connected with Circular Domain

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 670 ◽  
Author(s):  
Lei Shi ◽  
Qaiser Khan ◽  
Gautam Srivastava ◽  
Jin-Lin Liu ◽  
Muhammad Arif
Keyword(s):  
Integral Operator ◽  
Starlike Functions ◽  
Circular Domain ◽  
Coefficient Estimates ◽  
The Past

Starlike functions have gained popularity both in literature and in usage over the past decade. In this paper, our aim is to examine some useful problems dealing with q-starlike functions. These include the convolution problem, sufficiency criteria, coefficient estimates, and Fekete–Szegö type inequalities for a new subfamily of analytic and multivalent functions associated with circular domain. In addition, we also define and study a Bernardi integral operator in its q-extension for multivalent functions. Furthermore, we will show that the class defined in this paper, along with the obtained results, generalizes many known works available in the literature.

scholarly journals Multivalent Functions Related with an Integral Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Syed Ghoos Ali Shah ◽  
Saqib Hussain ◽  
Saima Noor ◽  
Maslina Darus ◽  
Ibrar Ahmad
Keyword(s):  
Integral Operator ◽  
Hadamard Product ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Rate Of Growth ◽  
Convex And Starlike Functions

In this present paper, we introduce and explore certain new classes of uniformly convex and starlike functions related to the Liu–Owa integral operator. We explore various properties and characteristics, such as coefficient estimates, rate of growth, distortion result, radii of close-to-convexity, starlikeness, convexity, and Hadamard product. It is important to mention that our results are a generalization of the number of existing results in the literature.

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.

COEFFICIENT ESTIMATES FOR SOME CLASSES OF FUNCTIONS ASSOCIATED WITH -FUNCTION THEORY

2017 ◽  
Vol 95 (3) ◽  
pp. 446-456 ◽  
Author(s):  
SARITA AGRAWAL
Keyword(s):  
Convex Functions ◽  
Representation Theorem ◽  
Function Theory ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Coefficient Estimates

For every $q\in (0,1)$, we obtain the Herglotz representation theorem and discuss the Bieberbach problem for the class of $q$-convex functions of order $\unicode[STIX]{x1D6FC}$ with $0\leq \unicode[STIX]{x1D6FC}<1$. In addition, we consider the Fekete–Szegö problem and the Hankel determinant problem for the class of $q$-starlike functions, leading to two conjectures for the class of $q$-starlike functions of order $\unicode[STIX]{x1D6FC}$ with $0\leq \unicode[STIX]{x1D6FC}<1$.

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

Applications on a subclass of β-uniformly starlike functions connected with q-Borel distribution

2021 ◽  
Author(s):  
Sheza M. El-Deeb ◽  
G. Murugusundaramoorthy
Keyword(s):  
Starlike Functions ◽  
Coefficient Estimates ◽  
Linear Combinations ◽  
Distortion Theorems ◽  
Uniformly Starlike Functions ◽  
Uniformly Starlike

The aim of this paper is to define the operator of [Formula: see text]-derivative based upon the Borel distribution and by using this operator, we familiarize a new subclass of [Formula: see text]-uniformly starlike functions [Formula: see text]-[Formula: see text] Further, we obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-to-convexity, starlikeness and convexity for functions [Formula: see text]-[Formula: see text] We also determine the second Hankel inequality for functions belonging to this subclass.

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 On Certain Subclass of Harmonic Starlike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Y. Lashin
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
New Class ◽  
Distortion Bounds ◽  
Harmonic Starlike

Coefficient conditions, distortion bounds, extreme points, convolution, convex combinations, and neighborhoods for a new class of harmonic univalent functions in the open unit disc are investigated. Further, a class preserving integral operator and connections with various previously known results are briefly discussed.

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