*Correspondence: [email protected]; [email protected] The National Academy of Sciences, ROK, Seoul, 137-044, Korea Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, Korea Abstract Recently we established the Knaster, Kuratowski, and Mazurkiewicz (KKM) theory on abstract convex spaces. In our research, we noticed that there are quite a few generalizations and a...

For convex subsets X of a topological vector space E, we show that a KKM principle implies a Fan-Browder type fixed point theorem and that this theorem implies generalized forms of the Sion minimax theorem. The von Neumann-Sion minimax theorem is fundamental in convex analysis and in game theory. von Neumann [8] proved his theorem for simplexes by reducing the problem to the 1-dimensional cases...

In this paper, after reviewing some results in minimal space, some new results in this setting are given. We prove a generalized form of the Fan-KKM typetheorem in minimal vector spaces. As some applications, the open type of matching theorem and generalized form of the classical KKM theorem in minimal vector spaces are given.

In this paper, the first part, we establish the fixed point theorems for a k-set contraction map on the class Q(X,Y ), (see [1]) . The second part, we generalize the KKM pproperty on a convex set [2] to the KKM∗ property on a nearly-convex set, and then we establish fixed point theorems, matching theorems and variational inequalities for this class. Mathematics Subject Classification: 47H10, 54...

We present the results of a numerical investigation of the turbulent kinematic dynamo problem in a high Prandtl number regime. The scales of the magnetic turbulence we consider are far smaller than the Kolmogorov dissipative scale, so that the magnetic wavepackets evolve in a nearly smooth velocity field. Firstly, we consider the Kraichnan-Kazantsev model (KKM) in which the strain matrix is tak...

We introduce the notion of relaxed ρ-θ -η-invariant pseudomonotone mappings, which is weaker than invariant pseudomonotone maps. Using the KKM technique, we establish the existence of solutions for variational-like inequality problems with relaxed ρ-θ -η-invariant pseudomonotone mappings in reflexive Banach spaces. We also introduce the concept of ρθ -pseudomonotonicity for bifunctions, and we ...

We use a concept of abstract convexity to define the almost S-KKM C property, al-S-KKM C X, Y family, and almost Φ-spaces. We get some new approximate fixed point theorems and fixed point theorems in almost Φ-spaces. Our results extend some results of other authors. Copyright q 2009 Tong-Huei Chang et al. This is an open access article distributed under the Creative Commons Attribution License,...

We prove some results on maximal elements using the KKM-map principle.