1) Invent sufficient conditions for the existence and/or convergence theorems of fixed points for new nonlinear single valued mappings and multi-valued operators defined by simulation functions via the topological and numerical methods. Some illustrative examples are furnished which demonstrate the validity of the hypotheses and degree of utility of our results.
2) We slightly modify their notion of simulation function and we investigate the existence and uniqueness of fixed points of nonlinear single valued and multi-valued operators using this kind of control functions. Some illustrative examples to claim that our results properly generalizes some results in literature are given.
3) We show a variety of cases in which our results can be applied, that is, we show that simulation functions and others control functions are very useful to express very different kinds of contractivity conditions in an only way.
4) We describe how to use our results in order to guarantee existence and uniqueness of solution of various nonlinear problems.
