Relationships between Robinson metric regularity and Lipschitz-like behavior of implicit multifunctions

By constructing some suitable examples, Jeyakumar and Yen (2004) [1] have shown that the Robinson metric regularity (Rmr) and the Lipschitz-like property (Llp) of implicit multifunctions are not equivalent. This paper clarifies relationships between the two properties of implicit multifunctions. It turns out that the (reasonable) sufficient conditions for having (Rmr) ⇒⇒ (Llp) are quite different from those for the validity of the reverse implication. The implicit function theorem due to Yen and Yao (2009) [2] serves as a tool for our analysis of (Rmr) and (Llp).