|本期目录/Table of Contents|

[1]QIU Song liang,CHEN Shi yong.On the Best Case of a Kind of Upper Bounds for φK-Distortion Function[J].浙江理工大学学报,2014,31-32(自科5):565-570.
　QIU Song liang,CHEN Shi yong.On the Best Case of a Kind of Upper Bounds for  φ K Distortion Function[J].Journal of Zhejiang Sci-Tech University,2014,31-32(自科5):565-570.
点击复制

On the Best Case of a Kind of Upper Bounds for φK-Distortion Function()
分享到：

浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第31-32卷
期数:
2014年自科5期
页码:
565-570
栏目:
(自科)数学及应用
出版日期:
2014-09-10

文章信息/Info

Title:
On the Best Case of a Kind of Upper Bounds for  φ K Distortion Function
文章编号:
1673-3851 (2014) 05-0565-06
作者:
QIU Song liang;  CHEN Shi yong
Author(s):
QIU Song liang;  CHEN Shi yong
School of Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
upper bound estimation;  Hübner s inequality;  Hersch Pfluger Distortion function;  quasiconformal Schwarz lemma
分类号:
O156.4
文献标志码:
A
摘要:
This paper studies the optimal index  α  of of  M(r )=2π( r′) 2κ(r)κ′(r )+log  r  in upper bound estimation in famous Hübner inequation in quasiconformal theory, gains estimated values of upper and lower bounds when max { c : inequality  M(r)<(r′) c log 4 is established for all r ∈ (0,1)}, and proves min { c: M(r)>(1-r) c  log 4 is established for all  r ∈(0,1)}=1. Thus, very important upper bound of Hersch Pfluger deviation function φ K(r)  in quasiconformal theory and corresponding explicit quasiconformal Schwarz lemma are improved.

参考文献/References:

［1］ Abramowitz M, Stegun I A. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables［M］. New York: Dover, 1965: 253-294.
［2］ Qiu S L, Vuorinen M. Handbook of Complex Analysis: Special Function in Geometric Function Theory［M］. Elsevier B V, 2005: 621-659.
［3］ Anderson G D, Vamanamurthy M K, Vuorinen M. Conformal Invariants, Inequalities, and Quasiconformal Mappings［M］. New York: John Wiley & Sons, 1997: 32-47.
［4］ Letho O, Virtanen K I. Quasiconformal Mappings in the Plane［M］. 2nd ed. New York: Springer, 1973.
［5］ Anderson G D, Qiu S L, Vamanamurthy M K. Grtzsch ring and quasiconformal distortion function［J］. Hokkaido J Math, 1995, 24: 551-566.
［6］ Anderson G D, Qiu S L, Vamanamurthy M K, et al. Generalized elliptic integrals and modular equations［J］. Pacific J Math, 2000, 192(1): 1-37.
［7］ Hersch  J, Pfluger A. Généralisation du lemma de Schwarz et du principe de la mesure harmonique pour les functions pseudo analytique［J］. C R Acad Bulgare Sci, 1952, Paris 234: 43-45.
［8］ Hübner O. Remarks on a paper of Lawrynowicz on quasiconformal mappings［J］. Bull de l Acad Polon des Sci, 1970, 18(2): 183-186.
［9］ Qiu S L, Amanamurthy M K, Vuorinen M. Some inequalities for the HerschPfluger distortion function［J］. J Ineq Appl, 1999, 4(2): 115-139.
［10］Qiu S L, Vuorinen M. Submultiplicative properties of the φ K distortion functions［J］. Studia Math, 1996, 117(3): 225-242.
［11］Qiu S L. Singular values, quasiconformal maps and the Schottky upper bound［J］. Sci China Ser A, 1998, 28(7): 606-612.
［12］Zhang X H, Wang G D, Chu Y M, et al. Distortion theorems of plane quasiconformal mappings［J］. J Math Anal Appl, 2006, 324: 60-65.
［13］Qiu S L, Ren L Y. Sharp estimates for Hübners upper bound function with applications［J］. Appl Math J Chinese Univ. 2010, 25(2): 227-235.
［14］Alzer H, Qiu S L. Monotonicity theorems and inequalities for the complete elliptic integrals［J］. J of Computational and Applied Mathematics, 2004, 172: 289-312.

备注/Memo

备注/Memo:
Received date：2014-03-27
Foundation item：This research is supported by the NSF of P. R. China(Grant No.114329A4A11652)
Introduction of the first author： QIU Songliang(1957-), Male, Fuyang, Zhejiang; Professor, Mathematics
更新日期/Last Update: 2014-09-26