
Journal of Convex Analysis 19 (2012), No. 4, 955973 Copyright Heldermann Verlag 2012 LyusternikGraves Theorem and Fixed Points II Asen L. Dontchev Mathematical Reviews, Ann Arbor, MI 481078604, U.S.A., Bulgaria ald@ams.org Hélène Frankowska CNRS  Institut de Mathématiques, Université P. et M. Curie, 4 place Jussieu, 75252 Paris, France frankowska@math.jussieu.fr This work continues the studies in our previous paper ["LyusternikGraves theorem and fixed points", Proc. Amer. Math. Soc. 139 (2011) 521534]. It is written as a separate paper which extends the previous one in the direction of closing the gap between LyusternikGraves theorems and fixed point theorems. Here we introduce a new definition of global metric regularity on a set and associated definitions of Aubin continuity and linear openness that are equivalent to metric regularity on the same sets and with the same constant. When the sets are neighborhoods of a point in the graph of the mapping, these definitions reduce to the well studied properties at a point. We present LyusternikGraves type theorems in metric spaces for singlevalued and setvalued perturbations, and show that they can be derived from, and some of them are even equivalent to, corresponding setvalued fixed point theorems. Keywords: Setvalued analysis, metric regularity, Aubin property, linear openness, contraction mapping, LyusternikGraves theorem, Milyutin theorem. MSC: 49J53, 47J07, 58C15, 49K40, 90C31 [ Fulltextpdf (174 KB)] for subscribers only. 