Construction of convex solutions for the second type of Feigenbaum's functional equations  

作　　者：SI JianGuo & ZHANG Min School of Mathematics, Shandong University, Jinan 250100, China 

出　　处：《Science China Mathematics》2009年第8期1617-1638,共22页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 10871117);Natural Science Foundation of Shandong Province (Grant No. Y2006A07)

摘　　要：In this paper, convex solutions for the second type of Feigenbaum's equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existence and uniqueness of continuous convex solutions, C1-convex solutions and C2-convex solutions of the above equation.In this paper, convex solutions for the second type of Feigenbaum’s equation f (x) = λ1 f (f (λx)), 0 < λ < 1, f (0) = 1, 0 f (x) 1, x ∈ [0, 1] are investigated. Using constructive methods, we discuss the existence and uniqueness of continuous convex solutions, C1-convex solutions and C2-convex solutions of the above equation.

关 键 词：the SECOND TYPE of Feigenbaum’s functional equations CONSTRUCTIVE method initial function CONVEX SOLUTIONS 

分 类 号：O174.13[理学—数学]