On Implicit Multifunction Theorems |
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| Affiliation: | (1) Institut de Mathématiques de Toulouse UMR CNRS 5219, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse cedex 4, France;(2) ENSET D’Oran, BP 1523, El Ménaouer, 31000 Oran, Algeria |
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| Abstract: | We give implicit multifunction results generalizing to multifunctions the Robinson’s implicit function theorem (Robinson, Math Oper Res 16(2):292–309, 1991). To this end, we use parametric error bounds estimates for a suitable function refining the one given in Azé and Corvellec (ESAIM Control Optim Calc Var 10:409–425, 2004). Sharp approximations of the implicit multifunctions are given extending the results of Nachi and Penot (Control Cybernet 35:871–901, 2005). Dedicated to Boris Mordukhovich in honour of his 60th birthday. |
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| Keywords: | Metric regularity Implicit multifunction theorems Strong slope |
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