On the convergence of two-step methods generated by point-to-point operators (Q5906391)

A common solution \(x^*\) of the sequence of nonlinear operator equations \(F_n(x)= 0\), \(n\geq 0\), is to be approximated. Two-step methods generated by point-to-point operators are applied. Iterations of this type have a great importance in optimization, stability analysis and many other fields of applied mathematics. The author proves convergence and gives an error analysis, using the theory of majorants in Banach spaces in the well-known matter of Kantorovich. The monotone convergence is also examined in a partially ordered topological space. Some applications are given to nonlinear integral equations of Uryson-type with special kernels.