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- W2362849163 abstract "We consider the difference equation xn+1=x(n+1)=x(n-k)/1+f(xn)g(xn),k∈Z+,n=k,k+1,…,where fg is a class of increasing continuous functions,which includes all functions of the form f(x)g(x)=αlogx or f(x)g(x)=αxβ for any α0 and β0.We prove that any solution of the equation with initial values(x0,x1,…,xk)∈ Rk+1+ is stable.And when k is an odd,the set of initial values such that corresponding solutions of converge to(a0,a1,…,ak-1,ak) is the set of points of the form(y0,y1,…,yk-1,yk)∈[a0,+∞)×[a1,+∞)×…×[ak-1,+∞)×[ak,+∞) such that yi+1=hi(yi) and hi∶[ai,+∞)→[ai+1,+∞) is an unique continuous increasing function for all ai≥0 (i=0,2,…,k-1)." @default.
- W2362849163 created "2016-06-24" @default.
- W2362849163 creator A5044605015 @default.
- W2362849163 date "2011-01-01" @default.
- W2362849163 modified "2023-09-27" @default.
- W2362849163 title "Convergent Properties of Solutions of Higher Order Difference Equation x_(n+1)=x_(n+1)=x_(n-k)/1+f(x_n)g(x_n)" @default.
- W2362849163 hasPublicationYear "2011" @default.
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