MONOTONICITY AND INEQUALITIES FOR THE GENERALIZED DISTORTION FUNCTION

被引：0
作者：
Ma, Xiaoyan [1 ]
Chu, Yuming [2 ]
Wang, Fei [1 ]
机构：
[1] Zhejiang Sci Tech Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China
[2] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2013年 / 33卷 / 06期
关键词：
generalized modular equation; generalized eta-distortion function; monotonicity; inequality; COMPLETE ELLIPTIC INTEGRALS; QUASI-CONFORMAL MAPPINGS; MODULAR EQUATIONS; SCHOTTKYS-THEOREM; BOUNDS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The authors prove some monotonicity properties of functions involving the generalized Agard distortion function eta(K)(a, t), and obtain some inequalities for eta(K)(a, t) and relative distortion functions.
引用
收藏
页码：1759 / 1766
页数：8
相关论文
共 21 条
  • [1] Modular equations and distortion functions
    Anderson, G. D.
    Qiu, S. -L.
    Vuorinen, M.
    [J]. RAMANUJAN JOURNAL, 2009, 18 (02) : 147 - 169
  • [2] DISTORTION FUNCTIONS FOR PLANE QUASICONFORMAL MAPPINGS
    ANDERSON, GD
    VAMANAMURTHY, MK
    VUORINEN, M
    [J]. ISRAEL JOURNAL OF MATHEMATICS, 1988, 62 (01) : 1 - 16
  • [3] Generalized elliptic integrals and modular equations
    Anderson, GD
    Qiu, SL
    Vamanamurthy, MK
    Vuorinen, M
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 2000, 192 (01) : 1 - 37
  • [4] Anderson GD, 1997, CONFORMAL INVARINANT
  • [5] RAMANUJANS THEORIES OF ELLIPTIC FUNCTIONS TO ALTERNATIVE BASES
    BERNDT, BC
    BHARGAVA, S
    GARVAN, FG
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (11) : 4163 - 4244
  • [6] SOME BOUNDS FOR THE COMPLETE ELLIPTIC INTEGRALS OF THE FIRST AND SECOND KINDS
    Guo, Bai-Ni
    Qi, Feng
    [J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2011, 14 (02): : 323 - 334
  • [7] SOME INEQUALITIES FOR THE GENERALIZED DISTORTION FUNCTIONS
    Ma, Xiao-Yan
    Wang, Miao-Kun
    Zhong, Gen-Hong
    Qiu, Song-Liang
    Chu, Yu-Ming
    [J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2012, 15 (04): : 941 - 954
  • [8] Some inequalities for the generalized linear distortion function
    Ma Xiao-yan
    Qiu Song-liang
    Zhong Gen-hong
    Chu Yu-ming
    [J]. APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B, 2012, 27 (01) : 87 - 93
  • [9] The distortion theorem for quasiconformal mappings, Schottky's theorem and holomorphic motions
    Martin, GJ
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (04) : 1095 - 1103
  • [10] Qiu SL, 2005, HANDBOOK OF COMPLEX ANALYSIS: GEOMETRIC FUNCTION THEORY, VOL 2, P621
123