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.

In this paper, the author considers generalized minimax theorems for vector set-valued mappings using Fan-KKM theorem on nonconvex domains of Hausdorff topological vector spaces.

Based on the G-H-KKM selections, some nonempty intersection theorems and their applications to minimax inequalities are presented.

The aim of this article is obtain a Krasnoselskĭı cone compression theorem for multimaps in the class S-KKM.