Positive Solutions And Iterative Approximations For A Nonlinear Two-dimensional Fourth-order Difference System With Multiple Delays

The purpose of this paper is to study the below nonlinear two-dimensional fourth-order difference system with multiple delaysUsing the Banach fixed point theorem and a few new analysis techniques, we show the existence of uncountable many positive solutions for the system, suggest Mann iterative algorithms and discuss the error estimates between the positive solutions and iterative sequences generated by the Mann iterative algorithms. Five examples to illustrate the results are included.The main content of this article consists four parts. The first part is an introduction and preliminaries, which introduces that many scholars have an increasing interest in the study of difference system in recent years and the development of this branch of nonlinear difference system is introduced. At the beginning, a large number of theorems which appear in the literature are cited to discuss, and it provides a good inspiration for constructing the nonlinear differential equations of this article. The relevant symbols and formulas are provided to prepare for the following theorems, and it is also easy for readers to read and understand. The second part of this paper is composed by five theorems. The goal is to study the existence of uncountable many positive solutions for the difference system and establish their iterative approximations and discuss the error estimates between the positive solutions and iterative approximations. These theorems which are established are based on five different values of the coefficient of the difference equations. At the whole number field, make -1 and +1 as the point of Demarcation to discuss. With the general, it is ensure that the real number in the whole domain is meaningful. While the Mann iterative algorithm and Banach fixed point theorem are used to discuss the related problems of the nonlinear difference systems, and corresponding limit conditions and primitive functions are given for each theorem. The third part includes some examples, which corresponds with the theorems to illustrate the validity of the conclusions. The conditions of Theorems are met while ensuring that the difference equation possesses multiple uncountable positive solutions. The last part of this article is the references.