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

Abstract EN

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 ∈ 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 2 → X 1 and t 2 : X 1 × X 2 → X 2 are discussed and an application to a system of nonlinear integral equations is given.