scholarly journals Phragmén-Lindelöf theorems for subharmonic functions on the unit disk.

1988 ◽  
Vol 62 ◽  
pp. 269 ◽  
Author(s):  
Robert D. Bermann ◽  
William S. Cohn
Keyword(s):  
Unit Disk ◽  
Subharmonic Functions

On new parametric representations of certain classes of subharmonic functions in the unit disk

2020 ◽  
pp. 65-72
Author(s):  
Romi Shamoyan
Keyword(s):  
Unit Disk ◽  
Parametric Representation ◽  
Subharmonic Functions

We define new spaces of subharmonic functions in the unit disk and provide characterizations of these new classes of functions via parametric representation.

The Yukawa Potential Function and Reciprocal Univalent Function

2013 ◽  
Vol 3 (2) ◽  
pp. 197-202
Author(s):  
Amir Pishkoo ◽  
Maslina Darus
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Potential Function ◽  
Univalent Function ◽  
Open Problem ◽  
Yukawa Potential ◽  
Reciprocal Theorem ◽  
Problem Statement ◽  
Fundamental Forces

This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

On the non-admissible subharmonic functions

1978 ◽  
Vol 64 (1) ◽  
pp. 15-20
Author(s):  
Victor Anandam
Keyword(s):  
Subharmonic Functions

On a Subclass of Univalent Harmonic Mappings Convex in the Imaginary Direction

2020 ◽  
pp. 445-454
Author(s):  
Deepali Khurana ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Imaginary Axis ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Distortion Bounds ◽  
Univalent Harmonic Mappings

In the present article, we consider a class of univalent harmonic mappings, $\mathcal{C}_{T} = \left\{ T_{c}[f] =\frac{f+czf'}{1+c}+\overline{\frac{f-czf'}{1+c}}; \; c>0\;\right\}$ and $f$ is convex univalent in $\mathbb{D}$, whose functions map the open unit disk $\mathbb{D}$ onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class.

Coefficient inequalities related with typically real functions

2020 ◽  
Vol 70 (4) ◽  
pp. 829-838
Author(s):  
Saqib Hussain ◽  
Shahid Khan ◽  
Khalida Inayat Noor ◽  
Mohsan Raza
Keyword(s):  
Unit Disk ◽  
Real Functions ◽  
Coefficient Inequalities ◽  
Typically Real ◽  
Class Of Functions ◽  
Typically Real Functions

AbstractIn this paper, we are mainly interested to study the generalization of typically real functions in the unit disk. We study some coefficient inequalities concerning this class of functions. In particular, we find the Zalcman conjecture for generalized typically real functions.

scholarly journals Some subordination involving polynomials induced by lower triangular matrices

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Saiful R. Mondal ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Unit Disk ◽  
Triangular Matrices ◽  
Cesàro Mean ◽  
Cesaro Mean ◽  
Lower Triangular ◽  
Lower Triangular Matrices

Abstract The article considers several polynomials induced by admissible lower triangular matrices and studies their subordination properties. The concept generalizes the notion of stable functions in the unit disk. Several illustrative examples, including those related to the Cesàro mean, are discussed, and connections are made with earlier works.

Radius problems for univalent functions

2020 ◽  
Vol 26 (1) ◽  
pp. 111-115
Author(s):  
Janusz Sokół ◽  
Katarzyna Trabka-Wiȩcław
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Radius Problems ◽  
Radius Of Convexity

AbstractThis paper considers the following problem: for what value r, {r<1} a function that is univalent in the unit disk {|z|<1} and convex in the disk {|z|<r} becomes starlike in {|z|<1}. The number r is called the radius of convexity sufficient for starlikeness in the class of univalent functions. Several related problems are also considered.

scholarly journals Triangular ratio metric in the unit disk

2021 ◽  
pp. 1-27
Author(s):  
Oona Rainio ◽  
Matti Vuorinen
Keyword(s):  
Unit Disk ◽  
Triangular Ratio Metric
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