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[1]QIU Songliang,WU Haiqin.A double inequality for the modulus of the Gr tzsch ring in Rn[J].浙江理工大学学报,2018,39-40(自科1):103-107.
　QIU Songliang,WU Haiqin.A double inequality for the modulus of the Gr tzsch ring in Rn[J].Journal of Zhejiang Sci-Tech University,2018,39-40(自科1):103-107.
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A double inequality for the modulus of the Gr tzsch ring in Rn()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第39-40卷
期数:
2018年自科1期
页码:
103-107
栏目:
出版日期:
2017-12-31

文章信息/Info

Title:
A double inequality for the modulus of the Gr tzsch ring in Rn
文章编号:
1673-3851 (2018) 01-0103-04
作者:
QIU Songliang;  WU Haiqin
School of Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, China
Author(s):
QIU Songliang;  WU Haiqin
School of Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
n dimensional quasiconformal theory;  the Grtzsch ring;  modulus;  inequalities
分类号:
O174.55
文献标志码:
A
摘要:
Let r′=1－r2 and Mn(r) be the (conformal) modulus of the Gr tzsch Ring in the quasiconformal theory in Rn, for n≥3 and r∈(0,1). In this paper, a double inequality is obtained for the function H(r)≡r′2 Mn(r)Mn (r′)n－1+r2 Mn (r′)Mn(r)n－1, thus improving known bounds for H(r), and correcting an error in the proof of a related inequality for H(r) which was given in a monograph by G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen.

参考文献/References:

［1］ Anderson G D, Vamanamurthy M K, Vuorinen M. Conformal Invariants, Inequalities, and Quasiconformal Maps［M］. New York: John Wiley and Sons,1997.
［2］ Ahlfors L V. Lectures on Quasiconformal Mappings［M］. 2nd ed. American Mathematical Society,2005.
［3］ Anderson G D, Frame J S. Numerical estimates for a Grtzsch ring constant［J］. Constr Approx,1988,4:223-242.
［4］ Abramowitz M, Stegun I A(Eds.). Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables［M］. New York: Dover,1965.
［5］ Qiu S L, Vuorinen M. Handbook of Complex Analysis: Special Function in Geometric Function Theory: Volume 2［M］. Elsevier B V,2005:621-659.
［6］ Qiu S L, Vuorinen M. Some properties of the gamma and psi functions with applications［J］. Math Comput,2005,74(250):723-742.
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［8］ Anderson G D, Qiu S L, Vamanamurthy M K. Grtzsch ring and quasiconformal distortion functions［J］. Hokkaido Math J,1995,24(3):551-566.
［9］ Anderson G D, Vamanamurthy M K, Vuorinen M. Conformal invariants, quasiconformal maps, and special functions［M］//Quasiconformal Space Mappings. BerlinHeidelberg: SpringerVerlag,1992:1-19.
［10］ Anderson G D, Vamanamurthy M K, Vuorinen M. Inequalities for quasiconformal mappings in space［J］. Pacific J Math,1993,160:1-18.
［11］ Ikoma K. An estimate for the modulus of the Grtzsch ring in nspace［J］. Bull Yamagata Univ Natur Sci,1967,6:395-400.
［12］ Qiu S L, Vamanamurthy M K. Elliptic integrals and the modulus of Grtzsch ring［J］. PanAmer Math J,1995,5(2):41-60.
［13］ Vuorinen M. On the boundary behavior of locally Kquasiconformal mappings in space［J］. Ann Acad Sci Fenn Ser A I,1980,5:79-95.

备注/Memo

备注/Memo:
收稿日期： 2017-06-06
网络出版日期： 2017-12-11
基金项目： This research is supported by the NSF of P. R. China (1171307)
作者简介： QIU Songliang(1957-),
更新日期/Last Update: 2018-03-13