We investigate two types of semicontinuity for set-valued maps, Painlevé–Kuratowski semicontinuity and Cesari’s property (Q). It is shown that, in the context of convexvalued maps, the concepts related to Cesari’s property (Q) have better properties than the concepts in the sense of Painlevé–Kuratowski. In particular, we give a characterization of Cesari’s property (Q) by means of upper semicon...

We consider five different types of systems of generalized vector quasi-equilibrium problems and establish relationships among them by using different kinds of generalized pseudomonotonicities. We prove the existence of their solutions under lower semicontinuity for a family of multivalued maps involved in the formulation of these problems. The existence of solutions of these problems is also i...

Using the notion of formal ball, we present a few new results in the theory of quasi-metric spaces. With no specific order: every continuous Yoneda-complete quasi-metric space is sober and convergence Choquet-complete hence Baire in its d-Scott topology; for standard quasi-metric spaces, algebraicity is equivalent to having enough center points; on a standard quasi-metric space, every lower sem...

We say that a Tychonoff space X has computable z-radicals if for all ideals a of C(X), the smallest z-ideal containing a is generated as an ideal by all the s◦f , where f is in a and s is a continuous function IR −→ IR with s−1(0) = {0}. We show that every cozero set of a compact space has computable z-radicals and that a subset X of IR has computable z-radicals if and only if X is locally closed.

We say that a Tychonoff space X has computable z-radicals if for all ideals a of C(X), the smallest z-ideal containing a is generated as an ideal by all the s ◦ f , where f is in a and s is a continuous function IR −→ IR with s−1(0) = {0}. We show that every cozero set of a compact space has computable z-radicals and that a subset X of IR has computable z-radicals if and only if X is locally cl...

Small Bowel Motility Assessment by means of Wireless Capsule Video Endoscopy constitutes a novel clinical methodology in which a capsule with a micro-camera attached to it is swallowed by the patient, emitting a RF signal which is recorded as a video of its trip throughout the gut. In order to overcome the main drawbacks associated with this technique -mainly related to the large amount of visu...

In this paper we introduce the concepts of quasimonotone maps and pseudoconvex functions. Moreover, a notion of pseudomonotonicity for multi mappings is introduced; it is shown that, if a function f is continuous, then its pseudoconvexity is equivalent to the pseudomonotonicity of its generalized subdifferential in the sense of Clarke and Rockafellar and prove that a lower semicontinuous functi...