Singular Values and Real Fixed Points of One Parameter Family of Function zbz/（bz-1）

作     者：Mohammad Sajid 

作者机构：College of Engineering Qassim University Buraidah AlQassim Saudi Arabia 

出 版 物：《Journal of Mathematics and System Science》 (数学和系统科学（英文版）)

年 卷 期：2014年第4卷第7期

页      面：486-490页

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 0822[工学-轻工技术与工程] 0701[理学-数学] 

主　　题：Critical values singular values fixed points 

摘      要：The purpose of this paper is to study the singular values and real fixed points of one parameter family of function,fλ（z）=λab2/b2-1,fλ（0）=λ/lnb for λ∈R／{0},z∈C and b〉 0 except b = 1. It is found that the function fλ（z） has infinitely many singular values for all b 〉 0 except b = 1. It is also shown that, for 0 〈 b 〈 1, all the critical values of fλ（z） lie in the left half plane while, for b 〉 1, lie in the right half plane. Further, it is seen that all these critical values are outside the open disk centered at origin and having radius ｜λ/lnb｜for all b 〉 0 except b = 1. Moreover, the real fixed points of fλ （z） and their nature are investigated.