Normal coderivative for multifunctions and implicit function theorems

In the framework of the theory of normal coderivative for multifunctions, new implicit function theorems are obtained. The main tools of the proofs are the Ekeland variational principle, a nonsmooth version of Fermat's rule, a sum rule, and the differential estimate for marginal functions established by B.S. Mordukhovich and Y. Shao [B.S. Mordukhovich, Y. Shao, Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc. 348 (1996) 1235–1280].