FIXED SET THEOREMS FOR DISCRETE DYNAMICS AND NONLINEAR BOUNDARY-VALUE PROBLEMS

We consider self-mappings of Hausdorff topological spaces which map compact sets to compact sets and establish the existence of invariant (fixed) sets. The fixed set results are used to provide fixed set analogues of well-known fixed point theorems. An algorithm is employed to compute the existence of fixed sets which are self-similar in a generalized sense. Some numerical examples are given. The utility of the abstract result is further illustrated via the study of a boundary value problem for a system of differential equations