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 uniquenes...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.展开更多
基金supported by National Natural Science Foundation of China(Grant No.10871117)Natural Science Foundation of Shandong Province(Grant No.Y2006A07)
文摘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.
