In this paper, we consider constrained multicriteria continuous location problems in two-dimensional spaces. In the literature, the continuous multicriteria location problem in two-dimensional spaces has received special attention in the last years, although only particular instances of convex functions have been considered. Our approach only requires the functions to be strictly quasiconvex an...

In this paper we extend naturally the scalarization proximal point method to solve multiobjective unconstrained minimization problems, proposed by Apolinario et al.[1], from Euclidean spaces to Hadamard manifolds for locally Lipschitz and quasiconvex vector objective functions. Moreover, we present a convergence analysis, under some mild assumptions on the multiobjective function, for two inexa...

In this paper, the author introduces the concept of the quasi-geometrically convex functions, gives Hermite-Hadamard’s inequalities for GA-convex functions in fractional integral forms and defines a new identity for fractional integrals. By using this identity, the author obtains new estimates on generalization of Hadamard et al. type inequalities for quasi-geometrically convex functions via Ha...

We fully characterize quasiconvex hulls for three arbitrary solenoidal (divergence free) wells in dimension three. With this aim we establish weak lower semicontinuity of certain functionals with integrands restricted to generic twodimensional planes and convex in (up to three) rank-2 directions within the planes. Within the framework of the theory of compensated compactness, the latter represe...

In this paper, we introduce several types of correspondences: weakly naturally quasiconvex, *-weakly naturally quasiconvex, weakly biconvex and correspondences with *–weakly convex graph and we prove some fixed point theorems for these kinds of correspondences. As a consequence, using a version of W.K. Kim’s quasi-point theorem, we obtain the existence of equilibria for a quasi-game.

We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in m×n , min(m,n) 6 2, then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit conve...

Solutions of variational problems under affine boundary conditions can be viewed equivalently as solutions of an implicit differential equation coupled with another equation that relates to quasiaffinity on the quasiconvex envelope of the integrand. In this work we derive conditions on an integrand and on its quasiconvex envelope which are sufficient for existence of solutions of a related lowe...