On the approximate solutions of constrained inverse Lipschitz function problems and inverse function theorems

✍ Scribed by Qinghai He; Fuchun Yang

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 415 KB
• Volume: 70
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2008.02.006

✦ Synopsis

We present a principle of approximate solutions of constrained inverse Lipschitz function problems. As corollaries and applications of the principle, we obtain a result of convergence of an approximate solutions sequence for the constrained problems, a conclusion relating direct and inverse images of upper and lower limits of a sequence of subsets, and several versions of inverse Lipschitz function theorems. Finally we give local uniqueness criteria for solutions to constrained nonlinear problems in finite dimension spaces.