Ball algorithms for constructing solutions of nonlinear operator equations

In the most general setting we extend the previous theory of the region contraction algorithm developed recently by several authors for solving nonlinear operator equations. It is demonstrated that the extended algorithm still possesses properties such as generating error bounds automatically, providing a computational test for the existence of solutions and being globally convergent under nominal conditions. As example of applications, we specialize the extended theory in particular to nonlinear operator equations of monotone type.