On The Existence Of Positive Solutions And Mann Iterative Schemes For A Two-dimensional Six Order Nonlinear Neutral Delay Difference System

In recent decades of time,more and more people began to pay attention to and explore neutral delay differential equations and systems,especially the existence of solution,stability,asymptotic behavior,bounded solution,oscillation,positive solution,periodic solution and error estimate about the different forms of linear and nonlinear neutral delay difference equation has received extensive attention and in-depth study.At home and abroad,many authors have made a lot of influential research achievements in this direction by using various fixed point theorems and some new techniques.This paper mainly introduces and studies the following two-dimensional six order nonlinear difference system with multiple delaysIn this paper,the Banach fixed point theorem and the Mann iterative algorithm are combined skillfully to study the existence of uncountable many positive solutions,the convergence of Mann iterative schemes and the error estimates between the approximate solutions and these positive solutions,respectively,for the above differential system in the nonempty closed and convex subset ?2w=1A(Nw,Mw)of Banach space.This paper includes nine theorems,and in the process of proof,according to the neutral in the different value,the corresponding mappings and Mann iterative approximation sequences are constructed respectively,and then those defined mappings are verified to meet the related conditions of the theorems.According to the corresponding tixed point theorems and the itreative algorithm,some sufficient conditions are obtained to ensure the differential system have multiple positive solutions,and at the same time give each component of such solutions is unbounded,also prove the iterative sequences and convergence of positive solutions of difference system(1.14).Finally nine nontrivial examples are constructed to demonstrate the application and importance of the results.