STABLE ITERATIVE PROCEDURES FOR A CLASS OF NONLINEAR INCREASING OPERATOR EQUATIONS IN BANACH SPACES

Abstract

In this paper, by using weak order-Lipschitz-condition, we introduce and study a class of nonlinear equations with increasing operators, and prove the existence and uniqueness theorems of solutions for this kind of nonlinear operator equations. We also discuss the convergence and stability of perturbed iterative algorithm for solving the nonlinear operator equations, and give some applications. Our results improve and generalize the corresponding results of recent works.