Let X be a convex subset of a locally convex topological vector space, let U⊂X be open with U¯ compact, let F:U¯→X be an upper semicontinuous convex valued correspondence with no fixed points in U¯∖U, let P be a compact absolute neighborhood retract, and let ρ:U¯→P be a continuous...

This short paper published in Games and Economic Behavior (July 2009) "In Memoriam" of David Gale, emphasizes the seminal role played by two lemmas of David Gale in the development of the foundations of General Equilibrium Theory.

In this paper, we establish a continuous selection theorem and use it to derive five equivalent results on the existence of fixed points, sectional points, maximal elements, intersection points and solutions of variational relations, all in topological settings without linear structures. Then,...

Nonlinear modified Leslie matrix models with different density-dependent birth and survival rates are analyzed. Conditions for the existence and uniqueness of a positive equilibrium state are discussed. In the case of exponential density dependence the conditions for local stability of a...

An interesting and challenging research subject in the field of nonlinear dynamics is the study of chaotic behavior in systems of more than two degrees of freedom. In this work we study fixed points, strange attractors, chaotic behavior and the problem of chaos control for complex Duffing's...

We study a model of sequential bargaining in which, in each period before an agreement is reached, the proposerʼs identity is randomly determined, the proposer suggests a division of a pie of size one, each other agent either approves or rejects the proposal, and the proposal is implemented if...

Principal curves have been defined Hastie and Stuetzle (JASA, 1989) as smooth curves passing through the middle of a multidimensional data set. They are nonlinear generalizations of the first principal component, a characterization of which is the basis for the principal curves definition. In...

In this paper we relax the convexity condition in some classical results on the existence of maximal elements in binary relations in order to generalize them. To do this, we replace the linear segments in the usual convexity with a family of previously fixed paths joining up each two points....