Approximating a Set-Valued Function Locally

摘要

Given a multi-valued mapping F, we address the problem of finding another multi-valued mapping H that agrees locally with F in some sense. We show that, contrary to the scalar case, introducing a derivative of F is hardly convenient. For the case when F is convex-compact-valued, we give some possible approximations, and at the same time we show their limitations. The present paper is limited to Informal demonstration of concepts and mechanisms. Formal statements and proofs will be published elsewhere.