A fixed point theorem without convexity

The purpose of this paper is to extend Himmelberg's fixed point theorem replacing the usual convexity in topological vector spaces by an abstract topological notion of convexity which generalizes classical convexity as well as several metric convexity structures found in the literature. We prove the existence, under weak hypotheses, of a fixed point for a compact approachable map and we provide sufficient conditions under which this result applies to maps whose values are convex in the abstract sense mentionned above

Continuous selections of multivalued mappings

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume

A Nonlinear Alternative for Approximable Maps : A Simple Proof.

We present a simple and direct proof for a nonlinear Leray-Schauder type alternative for a large class of condensing or compact set-valued maps, containing convex as well as nonconvex valued maps.ECONOMETRICS