Integral representation of a class of analytic functions

1970 ◽  
Vol 8 (3) ◽  
pp. 663-668
Author(s):  
B. E. Gopengauz
Keyword(s):  
Integral Representation ◽  
Analytic Functions

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.

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.

ON A NEW INTEGRAL REPRESENTATION OF RAMIFIED ANALYTIC FUNCTIONS

1995 ◽  
Vol 44 (3) ◽  
pp. 645-658
Author(s):  
B Yu Sternin ◽  
V E Shatalov
Keyword(s):  
Integral Representation ◽  
Analytic Functions

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 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 q–analogue of generalized Ruschweyh operator related to a new subfamily of multivalent functions

2019 ◽  
Vol 27 (2) ◽  
pp. 59-69
Author(s):  
Shahram Najafzadeh ◽  
Mugur Acu
Keyword(s):  
Integral Representation ◽  
Analytic Functions ◽  
Integral Operators ◽  
Arithmetic Mean ◽  
Coefficient Bounds

AbstractA new subfamily of p–valent analytic functions with negative coefficients in terms of q–analogue of generalized Ruschweyh operator is considered. Several properties concerning coefficient bounds, weighted and arithmetic mean, radii of starlikeness, convexity and close-to-convexity are obtained. A family of class preserving integral operators and integral representation are also indicated.

scholarly journals A Subfamily of Univalent Functions Associated with q-Analogue of Noor Integral Operator

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Muhammad Arif ◽  
Miraj Ul Haq ◽  
Jin-Lin Liu
Keyword(s):  
Integral Operator ◽  
Integral Representation ◽  
Linear Combination ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Coefficient Estimates ◽  
Arithmetic Means ◽  
Radius Of Starlikeness

The main objective of the present paper is to define a new subfamily of analytic functions using subordinations along with the newly defined q-Noor integral operator. We investigate a number of useful properties such as coefficient estimates, integral representation, linear combination, weighted and arithmetic means, and radius of starlikeness for this class.

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