Solvability of a forced third order nonlinear neutral delay difference equation

Abstract

This paper deals with the forced third order nonlinear neutral delay difference equation Δ3(x(n) + c(n)x(n - r)) + f(n, x(n - a), x(n - b)) = d(n), n≥n0. By means of the Banach fixed point theorem and some new techniques, we establish two sufficient conditions which ensure existence of a bounded positive solution for the equation, suggest the Mann type iterative scheme and discuss the error estimate between the bounded positive solution and the sequence generated by the Mann iterative scheme. Two nontrivial examples are also included.