Chain Rules for Linear Openness in Metric Spaces. Applications to Parametric Variational Systems

In this work we present a general theorem concerning chain rules for linear openness of set-valued mappings acting between metric spaces. As particular cases, we obtain classical and also some new results in this field of research, including the celebrated Lyusternik-Graves Theorem. The applications deal with the study of the well-posedness of the solution mappings associated to parametric variational systems. Sharp estimates for the involved regularity moduli are given.