On Positive Solutions And Mann Iterative Schemes Of A Third Order Difference System

This paper introduces and studies the following nonlinear three order difference system with multiple delays where,for any respectively, andBy utilizing the fixed point theorem and the iterative schemes, this paper discusses the existence of uncountably many positive solutions, conceive a few Mann iterative schemes for approximating these positive solutions,and prove their convergence and the error estimates, respectively, for the above difference system in the nonempty closed and convex subset A(N,M) of Banach space, and each component of this solution is unbounded. This text includes seven theorems, and in each proof of theorems, one or two mappings are constructed, and then the mappings which are used in the process of proof are proved to satisfy the conditions of the theorems. Finally, according to the Banach fixed point theorems and Mann iterative schemes, the conditions to ensure the existence of solutions of the system are obtained. In the end, seven nontrivial examples are constructed as applications of our results. The system described in this article differs from that of references in [1,2][7][10][12][15][26-28], the order of the difference system is higher, that form more general.