Sharp estimates for Hübner’s upper bound function with applications  

作　　者：QIU Song-Liang REN Liang-Yu 

机构地区：[1]School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2010年第2期227-235,共9页高校应用数学学报（英文版）（B辑）

基　　金：Supported by National 973 Project of China(2006CB708304);National Natural Science Foundation of China(10771195)

摘　　要：New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus. improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations.New better estimates, which are given in terms of elementary functions, for the function r →（2/π）（1 -r2）κ（r）κ′（r） ＋ logr appearing in Hubner＇s sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus. improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations.

关 键 词：ESTIMATE Hubner＇s inequality Hersch-Pfluger distortion function quasiconformal Schwarz lemma modular equation. 

分 类 号：O212.1[理学—概率论与数理统计] O157.5[理学—数学]