Positive Solutions and Mann Iterative Algorithms for a Second-Order Nonlinear Difference Equation

This paper deals with the second-order nonlinear neutral delay difference equation Δ(anh(xn-τ1n,xn-τ2n,…,xn-τmn)Δ(xn-qnxn-τ0))+f(n,xn-σ1n,xn-σ2n,…,xn-σkn)=bn, n≥n0. Using the Banach fixed point theorem, Mann iterative method with errors, and some new techniques, we prove the existence of uncountably...

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Bibliographic Details
Main Authors: Zeqing Liu, Xin Li, Shin Min Kang, Young Chel Kwun
Format: Article
Language:English
Published: Wiley 2016-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2016/8317567
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Summary:This paper deals with the second-order nonlinear neutral delay difference equation Δ(anh(xn-τ1n,xn-τ2n,…,xn-τmn)Δ(xn-qnxn-τ0))+f(n,xn-σ1n,xn-σ2n,…,xn-σkn)=bn, n≥n0. Using the Banach fixed point theorem, Mann iterative method with errors, and some new techniques, we prove the existence of uncountably many positive solutions and the convergence of the sequences generated by the Mann iterative method with errors relative to these solutions for the above equation. Six examples are included. Our results extend and improve essentially the known results in this field.
ISSN:2314-8896
2314-8888