New iterative methods to solve equations and systems in ordered spaces
The existence of solutions to the nonlinear equation \(Lu=Nu\) is studied by means of iterative methods. Here, \(L\) and \(N\) denote mappings between ordered spaces. The author firstly proves the existence of an upper solution and then applies the method of successive approximations that leads to the existence result. This result also implies some fixed point theorem. The example given at the end of the paper is somewhat academic.
scientific article; zbMATH DE number 1836642