一类迭代函数列的收敛性  

Some convergences on a class of iterative function sequences

作　　者：徐望斌 李邦荣 XU Wang-bin;LI Bang-rong(College of Mathematics and Statistics,Hubei Normal Univesity, Huangshi 435002,China)

机构地区：[1]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《湖北师范大学学报（自然科学版）》2018年第1期6-11,共6页Journal of Hubei Normal University：Natural Science

摘　　要：利用递归数列{a_n}:a_2=a_1+k,a_(n+2)=a_(n+1)+ka_n和{b_n}:b_(n+1)=1+k/b_n的通项公式求出函数f(x)=ax+b/cx+d(c≠0,ad-bc≠0)的n次迭代式,并利用其n次迭代式判断出其收敛性,得到其收敛的充要条件并严格证明,然后举例说明其优越性.In this paper,by using the general term formulas of two classes of recursive sequences{an}with a 2=a 1+k and an+2=an+1+kan,and{bn}with bn+1=1+1/bn,some n-th iteration formulas for some function f(x)=ax+b/cx+d(c≠0,ad-bc≠0)are found.Utilizing them,we obtain their convergence properties.Moreover,we introduce some necessary and sufficient conditions with strict proofs.Furthermore,some supportive examples are also given to illustrate the superiority of the obtained results.

关 键 词：函数迭代 递归数列 函数列 收敛性 

分 类 号：O17[理学—数学]