A boundary Schwarz lemma on the classical domain of type I

2017 ◽  
Vol 60 (7) ◽  
pp. 1239-1258 ◽  
Author(s):  
TaiShun Liu ◽  
XiaoMin Tang
Keyword(s):  
Schwarz Lemma ◽  
Type I ◽  
Classical Domain ◽  
Boundary Schwarz Lemma

scholarly journals A boundary Schwarz lemma for pluriharmonic mappings between the unit polydiscs of any dimensions

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 3151-3160
Author(s):  
Ziyan Huang ◽  
Di Zhao ◽  
Hongyi Li
Keyword(s):  
Harmonic Functions ◽  
Higher Dimensions ◽  
Schwarz Lemma ◽  
Boundary Schwarz Lemma ◽  
Bounded Harmonic Functions

In this paper, we present a boundary Schwarz lemma for pluriharmonic mappings between the unit polydiscs of any dimensions, which extends the classical Schwarz lemma for bounded harmonic functions to higher dimensions.

Schwarz lemma at the boundary on the classical domain of type ℐ𝒱

2019 ◽  
Vol 302 (1) ◽  
pp. 309-334
Author(s):  
Jianfei Wang ◽  
Taishun Liu ◽  
Xiaomin Tang
Keyword(s):  
Schwarz Lemma ◽  
Classical Domain

scholarly journals BOUNDARY SCHWARZ LEMMA FOR SOLUTIONS TO NONHOMOGENEOUS BIHARMONIC EQUATIONS

2019 ◽  
Vol 100 (3) ◽  
pp. 470-478 ◽  
Author(s):  
MANAS RANJAN MOHAPATRA ◽  
XIANTAO WANG ◽  
JIAN-FENG ZHU
Keyword(s):  
Schwarz Lemma ◽  
Biharmonic Equations ◽  
Boundary Schwarz Lemma

We establish a boundary Schwarz lemma for solutions to nonhomogeneous biharmonic equations.

Schwarz Lemma at the Boundary on the Classical Domain of Type $$\mathcal{III}$$

2020 ◽  
Vol 41 (3) ◽  
pp. 335-360
Author(s):  
Taishun Liu ◽  
Xiaomin Tang ◽  
Wenjun Zhang
Keyword(s):  
Schwarz Lemma ◽  
Classical Domain

scholarly journals Boundary Schwarz lemma and rigidity property for holomorphic mappings of the unit polydisc in Cn

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 2813-2818
Author(s):  
Ziyan Huang ◽  
Di Zhao ◽  
Hongyi Li
Keyword(s):  
Fixed Point ◽  
Unit Disk ◽  
Complex Plane ◽  
Complex Space ◽  
Holomorphic Mappings ◽  
Schwarz Lemma ◽  
Higher Dimensional ◽  
Rigidity Property ◽  
Boundary Schwarz Lemma

In this paper, we generalize the classical Schwarz lemma at the boundary from the unit disk D in the complex plane to the unit polydisc Dn in higher-dimensional complex space. Two boundary Schwarz lemmas for holomorphic mappings of Dn and corresponding rigidity properties are established without the restriction of the interior fixed point.

scholarly journals Boundary Schwarz lemma for holomorphic functions

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5553-5565
Author(s):  
Nafi Örnek ◽  
Burcu Gök
Keyword(s):  
Boundary Point ◽  
Unit Disc ◽  
Holomorphic Functions ◽  
Schwarz Lemma ◽  
Angular Derivative ◽  
Taylor Coefficient ◽  
Boundary Schwarz Lemma ◽  
Boundary Version

In this paper, a boundary version of Schwarz lemma is investigated. We take into consideration a function f (z) holomorphic in the unit disc and f (0) = 0 such that ?Rf? < 1 for ?z? < 1, we estimate a modulus of angular derivative of f (z) function at the boundary point b with f (b) = 1, by taking into account their first nonzero two Maclaurin coefficients. Also, we shall give an estimate below ?f'(b)? according to the first nonzero Taylor coefficient of about two zeros, namely z=0 and z0 ? 0. Moreover, two examples for our results are considered.

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