scholarly journals Uniformly Alpha-Quasi-Convex Functions Defined by Janowski Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Shahid Mahmood ◽  
Sarfraz Nawaz Malik ◽  
Sumbal Farman ◽  
S. M. Jawwad Riaz ◽  
Shabieh Farwa
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Analytic Functions ◽  
Janowski Functions ◽  
Convolution Properties ◽  
Inclusion Results

In this work, we aim to introduce and study a new subclass of analytic functions related to the oval and petal type domain. This includes various interesting properties such as integral representation, sufficiency criteria, inclusion results, and the convolution properties for newly introduced class.

New subclasses of analytic functions defined by convolution involving the hypergeometric function and the Owa–Srivastava operator

2019 ◽  
Vol 26 (3) ◽  
pp. 449-458
Author(s):  
Khalida Inayat Noor ◽  
Rashid Murtaza ◽  
Janusz Sokół
Keyword(s):  
Hypergeometric Function ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Integral Operators ◽  
Generalized Hypergeometric Functions ◽  
Convolution Properties ◽  
Appl Math ◽  
Inclusion Results

Abstract In the present paper we introduce a new convolution operator on the class of all normalized analytic functions in {|z|<1} , by using the hypergeometric function and the Owa–Srivastava operator {\Omega^{\alpha}} defined in [S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 1987, 5, 1057–1077]. This operator is a generalization of the operators defined in [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365] and [K. I. Noor, Integral operators defined by convolution with hypergeometric functions, Appl. Math. Comput. 182 2006, 2, 1872–1881]. Also we introduce some new subclasses of analytic functions using this operator and we discuss some interesting results, such as inclusion results and convolution properties. Our results generalize the results of [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365].

A generalized class of α-convex functions with respect to n-symmetric points

2021 ◽  
pp. 2250099
Author(s):  
A. Y. Lashin ◽  
F. Z. El-Emam
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Symmetric Points

In this paper, we investigate certain subclass of analytic functions on the open unit disc. This class generalizes the well-known class of [Formula: see text]-convex functions with respect to n-symmetric points. Some interesting properties such as subordination results, containment relations, integral preserving properties, and the integral representation for functions in this class are obtained.

scholarly journals Some Properties of a Generalized Class of Analytic Functions Related with Janowski Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
M. Arif ◽  
K. I. Noor ◽  
M. Raza ◽  
W. Haq
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Arc Length ◽  
Hankel Determinant ◽  
Janowski Functions ◽  
Coefficient Problems ◽  
Number Of Classes

We define a classT̃k[A, B,α,ρ] of analytic functions by using Janowski’s functions which generalizes a number of classes studied earlier such as the class of strongly close-to-convex functions. Some properties of this class, including arc length, coefficient problems, and a distortion result, are investigated. We also discuss the growth of Hankel determinant problem.

scholarly journals ON SOME SUBCLASSES OF CLOSE-TO-CONVEX FUNCTIONS OF ORDER $\alpha$ TYPE $\delta$

1998 ◽  
Vol 29 (1) ◽  
pp. 17-28
Author(s):  
KIIALIDA lNAYAT NOOR ◽  
AWATIF A. HENDI
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Function ◽  
Alpha Type

Let $Q_\lambda^*(\alpha, \delta)$ denote the class of analytic functions $f$ in the unit disc $E$, with $f(0)=0$, $f'(0) =1$ and satisfying the condition \[Re \left\{(1-\lambda)\frac{zf'(z)}{g(z)}+\lambda\frac{(zf'(z))'}{g'(z)}\right\}>\alpha,\] for $z\in E$, $g$ starlike function of order $\delta$ ($0 \le \delta \le 1$), $0\le \alpha \le 1$ and $\lambda$ complex with Re$\lambda\ge 0$. It is shown that $Q_\lambda^*(\alpha, \delta)$ with $\lambda\ge 0$ arc close-to-convex and hence univalent in $E$. Coeffiicient results, an integral representation for $Q_\lambda^*(\alpha, \delta)$ and some other propertie of $Q_\lambda^*(\alpha, \delta)$ are discussed. The class $Q_\lambda^*(\alpha, 1)$ is also investigated in some detail.

scholarly journals Generalizedk-Uniformly Close-to-Convex Functions Associated with Conic Regions

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Khalida Inayat Noor
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Problems ◽  
Multiplier Transformation ◽  
Inclusion Results

We define and study some subclasses of analytic functions by using a certain multiplier transformation. These functions map the open unit disc onto the domains formed by parabolic and hyperbolic regions and extend the concept of uniformly close-to-convexity. Some interesting properties of these classes, which include inclusion results, coefficient problems, and invariance under certain integral operators, are discussed. The results are shown to be the best possible.

scholarly journals On a class of analytic functions related to Robertson’s formula and subordination

2021 ◽  
Vol 27 (1) ◽  
Author(s):  
Adam Lecko ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Integral Representation ◽  
Analytic Functions ◽  
Boundary Point ◽  
Unit Disc ◽  
Starlike Functions ◽  
Analytic Formula ◽  
Growth Theorem

AbstractIn this paper, we define and study a class of analytic functions in the unit disc by modification of the well-known Robertson’s analytic formula for starlike functions with respect to a boundary point combined with subordination. An integral representation and growth theorem are proved. Early coefficients and the Fekete–Szegö functional are also estimated.

Convolution properties for certain subclass of analytic functions

2013 ◽  
Author(s):  
Norlyda Mohamed ◽  
Daud Mohamad ◽  
Shaharuddin Cik Soh
Keyword(s):  
Analytic Functions ◽  
Convolution Properties

scholarly journals Quasi-Hadamard Product of Certainω-Starlike andω-Convex Functions with respect to Symmetric Points

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Huo Tang ◽  
Guan-Tie Deng
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Symmetric Points

The main purpose of this paper is to derive some results associated with the quasi-Hadamard product of certainω-starlike andω-convex univalent analytic functions with respect to symmetric points.

Majorization of starlike and convex functions of complex order involving linear operators

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
K. Thilagavathi
Keyword(s):  
Linear Operator ◽  
Convex Functions ◽  
Analytic Functions ◽  
Linear Operators ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractThe main object of this present paper is to investigate the problem of majorization of certain class of analytic functions of complex order defined by the Dziok-Raina linear operator. Moreover we point out some new or known consequences of our main result.

scholarly journals Fekete–Szegö problem for certain subclasses of analytic functions

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Halit Orhan ◽  
Erhan Deniz ◽  
Murat Çağlar
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractIn this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order

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