Integral representation of a class of univalent functions

1976 ◽  
Vol 19 (1) ◽  
pp. 24-28 ◽  
Author(s):  
D. V. Prokhorov ◽  
B. N. Rakhmanov
Keyword(s):  
Integral Representation ◽  
Univalent Functions

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.

scholarly journals INTEGRAL REPRESENTATION OF SOLUTIONS OF AN ORDINARY DIFFERENTIAL EQUATION AND THE LOEWNER– KUFAREV EQUATION

2020 ◽  
pp. 28-39
Author(s):  
Olga V. ZADOROZHNAYA ◽  
◽  
Vladimir K. KOCHETKOV ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Integral Representation ◽  
Univalent Functions ◽  
Integral Form ◽  
Second Order ◽  
Partial Differential ◽  
Representation Of Solutions ◽  
Order Part

The article presents a method of integral representation of solutions of ordinary differential equations and partial differential equations with a polynomial right-hand side part, which is an alternative to the construction of solutions of differential equations in the form of different series. The method is based on the introduction of additional analytical functions establishing the equation of connection between the introduced functions and the constituent components of the original differential equation. The implementation of the coupling equations contributes to the representation of solutions of the differential equation in the integral form, which allows solving some problems of mathematics and mathematical physics. The first part of the article describes the coupling equation for an ordinary differential equation of the first order with a special polynomial part of a higher order. Here, the integral representation of the solution of a differential equation with a second-order polynomial part is indicated in detail. In the second part of the paper, we consider the integral representation of the solution of a partial differential equation with the polynomial second-order part of the Loewner–Kufarev equation, which is an equation for univalent functions.

scholarly journals Subclasses of Uniform Univalent Functions Associated with Srivastava and Attiya Operator

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1536
Author(s):  
Mohammad Yaseen ◽  
Irfan Ali ◽  
Sardar Muhammad Hussain ◽  
Jong-Suk Ro
Keyword(s):  
Integral Representation ◽  
Univalent Functions ◽  
Canonical Domain ◽  
Radius Problems ◽  
Analytic And Univalent Functions ◽  
Symmetrical Points

In this paper, we introduce new subclasses k−STs(p,β) and k−UKs(p,β) of analytic and univalent functions in the canonical domain associated with the Srivastava and Attiya operator. The radius problems of these subclasses regarding symmetrical points are investigated and compared with previous known results. Certain properties and conditions of these subclasses such as integral representation are also discussed in this work.

Certain Subclasses of Bi-Univalent Functions Involving Double Zeta Function

2015 ◽  
Vol 4 (4) ◽  
pp. 28-33
Author(s):  
Dr. T. Ram Reddy ◽  
◽  
R. Bharavi Sharma ◽  
K. Rajya Lakshmi ◽  
◽  
...  
Keyword(s):  
Zeta Function ◽  
Univalent Functions ◽  
Double Zeta

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

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