scholarly journals Lipschitz continuity of the distance ratio metric on the unit disk

Filomat ◽  
2013 ◽  
Vol 27 (8) ◽  
pp. 1505-1509 ◽  
Author(s):  
Slavko Simic
Keyword(s):  
Unit Disk ◽  
Lipschitz Continuity ◽  
Distance Ratio ◽  
The Distance Ratio Metric

scholarly journals Lipschitz conditions and the distance ratio metric

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 2137-2146 ◽  
Author(s):  
Slavko Simic ◽  
Matti Vuorinen
Keyword(s):  
Lipschitz Continuity ◽  
Distance Ratio ◽  
Lipschitz Conditions ◽  
The Distance Ratio Metric

We give a study of the Lipschitz continuity of M?bius transformations of a punctured ball onto another punctured ball in Rn with respect to the distance ratio metric. Some subtle methods are developed, helping to determine the best possible j-Lip constant in this case.

scholarly journals Sharp Lipschitz Constants for the Distance Ratio Metric

2015 ◽  
Vol 116 (1) ◽  
pp. 86 ◽  
Author(s):  
Slavko Simić ◽  
Matti Vuorinen ◽  
Gendi Wang
Keyword(s):  
Euclidean Space ◽  
Unit Ball ◽  
Unit Disk ◽  
Complex Plane ◽  
Distance Ratio ◽  
Möbius Transformations ◽  
Lipschitz Constants ◽  
The Distance Ratio Metric ◽  
Mobius Transformations

We study expansion/contraction properties of some common classes of mappings of the Euclidean space $\mathsf{R}^n$, $n\ge 2$, with respect to the distance ratio metric. The first main case is the behavior of Möbius transformations of the unit ball in $\mathsf{R}^n$ onto itself. In the second main case we study the polynomials of the unit disk onto a subdomain of the complex plane. In both cases sharp Lipschitz constants are obtained.

Quasiisometric mappings in the distance ratio metric in Banach spaces

2021 ◽  
Author(s):  
Tiantian Guan ◽  
Manzi Huang ◽  
Saminathan Ponnusamy ◽  
Xiantao Wang
Keyword(s):  
Banach Spaces ◽  
Distance Ratio ◽  
The Distance Ratio Metric

scholarly journals Lipschitz Continuity for the Solutions of Triharmonic Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Zhou Yu ◽  
Xiao Bing
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Dirichlet Boundary ◽  
Lipschitz Continuity ◽  
Boundary Value ◽  
Jordan Domain ◽  
Lipschitz Continuous ◽  
Equivalent Conditions

Let D be the unit disk in the complex plane C and denote T=∂D. Write Hom+T,∂Ω for the class of all sense-preserving homeomorphism of T onto the boundary of a C2 convex Jordan domain Ω. In this paper, five equivalent conditions for the solutions of triharmonic equations ∂z∂z¯3ω=ff∈CD¯ with Dirichlet boundary value conditions ωzz¯zz¯T=γ2∈CT,ωzz¯T=γ1∈CT and ωT=γ0∈Hom+T,∂Ω to be Lipschitz continuous are presented.

QUASICONFORMAL SOLUTIONS OF POISSON EQUATIONS

2015 ◽  
Vol 92 (3) ◽  
pp. 420-428 ◽  
Author(s):  
PEIJIN LI ◽  
JIAOLONG CHEN ◽  
XIANTAO WANG
Keyword(s):  
Unit Disk ◽  
Poisson Equation ◽  
Lipschitz Continuity ◽  
Poisson Equations ◽  
The Poisson Equation

The main aim of this paper is to establish the Lipschitz continuity of the $(K,K^{\prime })$-quasiconformal solutions of the Poisson equation ${\rm\Delta}w=g$ in the unit disk $\mathbb{D}$.

scholarly journals Hyperbolically Lipschitz continuity, area distortion and coefficient estimates for -quasiconformal harmonic mappings of unit disk

2021 ◽  
Vol 73 (2) ◽  
pp. 151-159
Author(s):  
Deguang Zhong ◽  
Wenjun Yuan
Keyword(s):  
Unit Disk ◽  
Lipschitz Continuity ◽  
Distortion Theorem ◽  
Harmonic Mappings ◽  
Coefficient Estimate ◽  
Coefficient Estimates ◽  
Area Distortion

UDC 517.51 We study the hyperbolically Lipschitz continuity, Euclidean and hyperbolic area distortion theorem,  and coefficient estimate for the classes of -quasiconformal harmonic mappings from the unit disk onto itself.

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.

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