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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 (fn(x))n∈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 t1:X1×X2→X1 and t2:X1×X2→X2 are discussed and an application to a system of nonlinear integral equations is given

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