Lipschitzian stability of fully parameterized generalized equations

This paper concerns the study of Lipschitzian stability of fully parameterized generalized equations in which both single-valued and set-valued functions depend on parameters. Various relationships between the Lipschitz-like and metric regularity properties of the solution mapping, the base mapping, or field mapping in the fully perturbed generalized equations are established by using the Dontchev–Hager Fixed Point Theorem. The implicit mapping theorem for metric regularity is also extended to fully parameterized generalized equations.