On the convergence of two-step methods generated by point-to-point operators

摘要

In this study we examine conditions for the convergence of two-step methods generated by point-to-point operators. Iterations of this type have a great importance in optimization theory, stability analysis of dynamic systems and many other fields of applied mathematics. The speed of convergence is also examined using the theory of majorants in a Banach space setting. The monotone convergence of these methods is also examined in a partially ordered topological space. Special cases of our results reduce to corresponding results already in the literature. In particular, relevant work can be found in [1, 2] and the references there. Some applications are also given to the solution of systems of nonlinear integral equations of Uryson-type.