Existence and Mann Iterative Methods with Errors of Nonoscillatory Solutions for a System of Second Order Nonlinear Neutral Delay Difference Equations
|School||Liaoning Normal University|
|Keywords||Nonoscillatory solution second-order neutral delay difference equation contraction mapping Mann iterative approximations|
This paper deals with the following system of second ordernonlinear neutral delay di?erence equations :where .with . A few su?cientconditions for the existence of nonoscillatory solutions and their Manntype iterative schemes with errors for the above equations are given,and the error estimates between the approximate solutions and thenonoscillatory solutions are also discussed. The su?cient conditionsfor existence of nonoscillatory solutions are expatiated through ninetheorems according to the range of value of constants p1,p2. Thesetheorems are mainly proofed as follows. At first, construct two map-pings T1 : A1→B, T2 : A2→B on two nonempty closed convexsubsets A1,A2 of the Banach space B. Using T1,T2, we construct acontraction mapping T = (T1,T2) and illuminate the mapping T is aself-mapping on subset A1×A2 by the method of classified discussion.Afterwards, make use of Banach contraction mapping theory to gaina unique fixed point (x,y)∈A1×A2 of mapping T, then the fixedpoint (x,y)∈A1×A2 is a solution of the above equations. In the lastsection, two examples are presented to illustrated that our works areproper generalizations of the corresponding results of Cheng  andZhang and Zhou .