A KKM space is an abstract convex space satisfying the KKM principle. We obtain variants of the KKM principle for KKM spaces related to weakly KKM maps and indicate some applications of them. These results properly generalize the corresponding ones in G-convex spaces and φA-spaces X,D; {φA}A∈〈D〉 . Consequently, results by Balaj 2004, Liu 1991, and Tang et al. 2007 can be properly generalized an...

Various types of φA-spaces (X,D; {φA}A∈〈D〉) are simply G-convex spaces. Various types of generalized KKM maps on φA-spaces are simply KKM maps on G-convex spaces. Therefore, our G-convex space theory can be applied to various types of φAspaces. As such examples, we obtain KKM type theorems and a very general fixed point theorem on φA-spaces. RESUMEN Varios tipos de φA-espacios (X,D; {φA}A∈〈D〉) ...

In this paper we prove a new combinatorial theorem for labellings of trees, and show that it is equivalent to a KKM-type theorem for finite covers of trees and to discrete and continuous fixed point theorems on finite trees. This is in analogy with the equivalence of the classical Sperner’s lemma, KKM lemma, and the Brouwer fixed point theorem on simplices. Furthermore, we use these ideas to de...

In this review, firstly, we recall Ky Fan’s contributions to the KKM theory based on his celebrated 1961 KKM lemma (or the Fan-KKM theorem). Secondly, we introduce relatively recent applications of the Fan lemma due to other authors in the 21st century. Finally, some historical remarks on related works are added.

A cross-sectional study was conducted to determine the risk factors of job-related depression in laboratory technicians in Hospital Universiti Sains Malaysia (HUSM) and Kementerian Kesihatan Malaysia (KKM) Hospitals in Kelantan, between September 2001 and February 2002. One hundred and two laboratory technicians from HUSM and 79 from KKM Hospitals were selected and 84 (82.4%) from HUSM and 71 (...

In this paper, a general version of the KKM theorem is derived by using the concept of generalized KKM mappings introduced by Chang and Zhang. By employing our general KKM theorem, we obtain a general minimax inequality which contains several existing ones as special cases. As applications of our general minimax inequality, we derive an existence result for saddle-point problems under general s...

In the present paper, we extend known KKM theorems and matching theorems for generalized KKM maps to G-convex spaces. From these results, we deduce generalized versions of main results of Kassay and Kolumbán [KK] and some others.

The partial KKM principle for an abstract convex space is an abstract form of the classical KKM theorem. In this paper, we derive generalized forms of the Ky Fan minimax inequality, the von Neumann-Sion minimax theorem, the von Neumann-Fan intersection theorem, the Fan-type analytic alternative, and the Nash equilibrium theorem for abstract convex spaces satisfying the partial KKM principle. Th...

Karasek's job strain model postulates that workers chronically exposed to adverse psychosocial work environment (high strain job)--high psychological job demands and low job control, including poor social support, increased physical demand and hazardous work condition--will eventually develop both physical illnesses such as cardiovascular diseases and psychological disorders such as depression....