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.

scholarly journals A Subclass of Analytic Functions Related tok-Uniformly Convex and Starlike Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Saqib Hussain ◽  
Akhter Rasheed ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Convolution Operator ◽  
Starlike Functions ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Open Unit Disc ◽  
Coefficient Inequalities ◽  
Uniformly Starlike Functions ◽  
Convex And Starlike Functions ◽  
Uniformly Starlike

We investigate some subclasses ofk-uniformly convex andk-uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed.

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 Certain Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
N. Magesh
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Hypergeometric Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Generalized Hypergeometric Functions ◽  
Uniformly Convex Functions

Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the classTSml(α,β,γ). In particular, we obtain integral means inequalities for the functionfthat belongs to the classTSml(α,β,γ)in the unit disc.

scholarly journals New classes of $k$-uniformly convex and starlike functions

2004 ◽  
Vol 35 (3) ◽  
pp. 261-266 ◽  
Author(s):  
Essam Aqlan ◽  
Jay M. Jahangiri ◽  
S. R. Kulkarni
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Radius Of Starlikeness ◽  
Distortion Bounds ◽  
Convex And Starlike Functions

Certain classes of analytic functions are defined which will generalize new, as well as well-known, classes of k-uniformly convex and starlike functions. We provide necessary and sufficent coefficient conditions, distortion bounds, extreme points and radius of starlikeness for these classes.

A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator

2019 ◽  
Vol 69 (4) ◽  
pp. 825-832 ◽  
Author(s):  
Shahid Khan ◽  
Saqib Hussain ◽  
Muhammad A. Zaighum ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Extreme Point ◽  
Convex Functions ◽  
Starlike Functions ◽  
Starlike Function ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions ◽  
New Class ◽  
Closure Theorems

Abstract Making use of Ruscheweyh q-differential operator, we define a new subclass of uniformly convex functions and corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain, coefficient estimates, closure theorems and extreme point for the functions belonging to this new class. The results are generalized to families with fixed finitely many coefficients.

scholarly journals A GENERALIZATION OF CERTAIN CLASS OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS

1995 ◽  
Vol 26 (2) ◽  
pp. 107-117
Author(s):  
M. K. AOUF ◽  
A. SHAMANDY
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Fractional Operators ◽  
Coefficient Estimates ◽  
Func Tions ◽  
Closure Theorems ◽  
Distortion Theorems ◽  
Radius Of Univalence

We introduce the subclass $T^*(A,B,n,a)$ ($-1 \le A < B\le 1$, $0 < B \le 1$, $n \ge 0$, and $0\le\alpha <1$) of analytic func;tions with negative coefficients by the operator $D^n$. Coefficient estimates, distortion theorems, closure theorems and radii of close-to-convexety, starlikeness and convexity for the class $T^*(A,B,n,a)$ are determined. We also prove results involving the modified Hadamard product of two functions associated with the class $T^*(A,B,n,a)$. Also we obtain Several interesting distortion theorems for certain fractional operators .of functions in the class $T^*(A,B,n,a)$. Also we obtain class perserving integral operator of the form \[F(z)=\afrc{c+1}{z^c}\int_0^z t^{c-1}f(t) dt, \quad c>-1\] for the class $T^*(A,B,n,a)$. Conversely when $F(z) \in T*(A,B,n,a)$, radius of univalence of $f(z)$ defined by the above equation is obtained.

scholarly journals Subclasses of uniformly convex and starlike functions associated with Bessel functions

2019 ◽  
Vol 43 (5) ◽  
pp. 2433-2443
Author(s):  
Muhammad NAEEM ◽  
Saqib HUSSAIN ◽  
F. Müge SAKAR ◽  
Tahir MAHMOOD ◽  
Akhter RASHEED
Keyword(s):  
Bessel Functions ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Convex And Starlike Functions

scholarly journals Subclasses of analytic functions with respect to symmetric and conjugate points

2011 ◽  
Vol 42 (1) ◽  
pp. 87-94
Author(s):  
C. Selvaraj ◽  
N. Vasanthi
Keyword(s):  
Analytic Functions ◽  
Starlike Functions ◽  
Conjugate Points ◽  
Coefficient Estimates ◽  
Convex And Starlike Functions

In this paper, we introduce new subclasses of convex and starlike functions with respect to other points. The coefficient estimates for these classes are obtained.

CLASSES OF k-UNIFORMLY CONVEX AND STARLIKE FUNCTIONS INVOLVING THE GENERALIZED FOX-WRIGHT FUNCTION

2016 ◽  
Vol 99 (7) ◽  
pp. 1081-1107
Author(s):  
Lakshminarayanan Vanitha ◽  
Chellakutti Ramachandran ◽  
Teodor Bulboacă
Keyword(s):  
Starlike Functions ◽  
Wright Function ◽  
Uniformly Convex ◽  
Convex And Starlike Functions
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