Nonlinear Dynamics, Fixed Points and Coupled Fixed Points in Generalized Gauge Spaces with Applications to a System of Integral Equations

We will discuss discrete dynamics generated by single-valued and multivalued operators in spaces endowed with a generalized metric structure. More precisely, the behavior of the sequence (f(n)(x))(n subset of N) of successive approximations in complete generalized gauge spaces is discussed. In the same setting, the case of multivalued operators is also considered. The coupled fixed points for mappings t(1) : X-1 x X-2 -> X-1 and t(2) : X-1 x X-2 -> X-2 are discussed and an application to a system of nonlinear integral equations is given.