Lipschitzian stability of fully parameterized generalized equations

Abstract

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.

Keywords:

• Generalized equation
• solution map
• (partial) metric regularity
• (partial) Lipschitz-like property

AMS Subject Classifications:

• 49J53
• 47H04
• 54C60

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of the People’s Republic of China [grant number 61663049]; [grant number 11461080]; [grant number 11261067].