The aim of this paper is to characterize in terms of scalar quasiconvexity the vector-valued functions which are K-quasiconvex with respect to a closed convex cone K in a Banach space. Our main result extends a wellknown characterization of K-quasiconvexity by means of extreme directions of the polar cone of K, obtained by Dinh The Luc in the particular case when K is a polyhedral cone generate...

In this paper, we introduce the class of multivalued relaxed μ quasimonotone operators and establish the existence of solutions of variational inequalities for such operators. This result is compared with a recent result of Bai et al on densely relaxed pseudomonotone operators. A similar comparison regarding an existence result of Luc on densely pseudomonotone operators is provided. Also, we in...

We establish some results concerning P{functions from the standpoint of abstract convexity. In particular, we show that the set of all P{functions on a segment is the least set closed under pointwise sum, supremum and convergence and containing the class of all nonnegative quasiconvex functions on that segment. Further, generalizations are derived of a recent inequality of Hadamard type for P{f...

We study the problem of characterizing quasiconvex hulls for three “solenoidal” (divergence free) wells in dimension three when the wells are pairwise incompatible. A full characterization for a generic regime is achieved by translating the problem into the language of H-measures, following recipes of Kohn and Smyshlyaev & Willis, in combination with certain ideas based on Šverák’s example of a...