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 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 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.

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 Bounded Doubly Close-to-Convex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Dorina Răducanu
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Coefficient Bounds ◽  
New Class ◽  
Radius Of Convexity ◽  
Distortion Theorems

We consider a new classCC(α,β)of bounded doubly close-to-convex functions. Coefficient bounds, distortion theorems, and radius of convexity for the classCC(α,β)are investigated. A corresponding class of doubly close-to-starlike functionsS*S(α,β)is also considered.

scholarly journals Radii of starlikeness and convexity for functions with fixed second coefficient defined by subordination

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 553-561 ◽  
Author(s):  
Rosihan Ali ◽  
Eun Cho ◽  
Kumar Jain ◽  
V. Ravichandran
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Radius Of Starlikeness ◽  
Uniformly Convex Functions ◽  
Lemniscate Of Bernoulli ◽  
Strongly Starlike Functions ◽  
Special Cases ◽  
Radius Of Convexity ◽  
Strongly Starlike

Several radii problems are considered for functions f (z) = z + a2z2 + ... with fixed second coefficient a2. For 0 ? ? < 1, sharp radius of starlikeness of order ? for several subclasses of functions are obtained. These include the class of parabolic starlike functions, the class of Janowski starlike functions, and the class of strongly starlike functions. Sharp radius of convexity of order ? for uniformly convex functions, and sharp radius of strong-starlikeness of order ? for starlike functions associated with the lemniscate of Bernoulli are also obtained as special cases.

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 $0\leq \unicode[STIX]{x1D6FC}<1$.

Some properties of the analytic functions with bounded radius rotation

2019 ◽  
Vol 28 (1) ◽  
pp. 85-90
Author(s):  
YASAR POLATOGLU ◽  
◽  
ASENA CETINKAYA ◽  
OYA MERT ◽  
◽  
...  
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Coefficient Estimate ◽  
Open Unit Disc ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
Bounded Radius Rotation

In the present paper, we introduce a new subclass of normalized analytic starlike functions by using bounded radius rotation associated with q- analogues in the open unit disc \mathbb D. We investigate growth theorem, radius of starlikeness and coefficient estimate for the new subclass of starlike functions by using bounded radius rotation associated with q- analogues denoted by \mathcal{R}_k(q), where k\geq2, q\in(0,1).

Some properties of a subclass of uniformly convex functions with negative coefficients

2008 ◽  
Vol 41 (2) ◽  
Author(s):  
M. K. Aouf ◽  
A. O. Mostafa
Keyword(s):  
Convex Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions

AbstractThe aim of this paper is to obtain coefficient estimates, distortion theorem, extreme points and radii of close - to - convexity, starlikeness and convexity for functions belonging to the subclass

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.

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