Kantorovich's Majorization and Functional Equations

Abstract

We consider systems of nonlinear difference equations arising when convergence analysis of an iterative method for solving operator equations in Banach spaces is carried out via Kantorovich's technique of majorization. The main challenge in this context is to determine the convergence domain of the corresponding majorant generator. As it turns out, dealing with this task leads to solution of functional equations of a certain kind. After considering several examples, we formulate two generic models and develop an approach to their solution.

Keywords:

• Operator equations
• Convergence analysis
• Nonlinear difference equations
• Functional equations