麦结华.关于迭代函数方程f2(x)=af(x)+bx的通解[J].数学研究及应用,1997,17(1):83~90
关于迭代函数方程f2(x)=af(x)+bx的通解
On General Solutions of the Iterated Functional Equation f2(x)=af(x)+bx
  
DOI:10.3770/j.issn:1000-341X.1997.01.017
中文关键词:  连续函数  迭代函数方程  动力系统  通解
英文关键词:continuous function  iterated functional equation  dynamical system  general solution.
基金项目:国家自然科学基金重点资助项目.
作者单位
麦结华 汕头大学数学研究所 
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中文摘要:
      设λ的二次三项式λ2-aλ-b的两个零点为λ1=r,λ2=s(a及b为实数).对0<r<s,r<0<s≠-r及r=s≠0这三种情形,J.Matkowski与Weinian Zhang在“Method of characteristics for functional equations in polynomial form”一文中给出了迭代函数方程f2(x)=af(x)+bx,对任x∈R;f∈C0
英文摘要:
      Let a and b be real numbers, and let the two zero points of the quadratic polynomial λ2-aλ-b of λ be λ1=randλ2=s. For the three cases 0 < r < s, r < 0 < s ≠- r , and r = s≠ 0 , J. Matkow skiand Weinian Zhang obtained general solutions of the iterated functional equation f2(x)=af(x)+bx, fo r a ll x ∈ R ; f ∈ C0(R , R ) (1) in their paper“Method of characteristics for functional equation in polynomial form ”, and proved that there are no solutions of equation (1) when r and s are not real numbers. For the case r =-s≠0, M. Kuczma has given general solutions of (1). And in this paper, for the remaining two cases r < s < 0 and rs = 0 , we give general solutions of (1). Moreover, we give a simple proof about general solutions of (1) in the case r<0
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