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.