,2005,28(2):127～130.) introduced the concept of finitely continuous(FC) spaces which contains many topological spaces with various convex structure in nonlinear analysis as special cases. In this paper,ased on Ding's concept and by using transfer open(closed) mappings,some applications of KKM type theorems,such as fixed point theorems and minimax inequalities are obtained in FC-spaces.
The convex structure of the set of measures μ such that the embedding KE*/E?L2(μ) is isometric (the set of such measures was described by de Brages) is considered.
Assumptions concerning an overall convex structure for the problem in the image space, the existence of interior points in certain sets, and the normality of the constraints are formulated.
The paper is devoted to the convergence properties of finite-difference local descent algorithms in global optimization problems with a special γ-convex structure.
Roughly speaking, a specific feature of these problems is that their nonconvex nucleus can be transformed into a complementary convex structure which can then be shifted to a subspace of much lower dimension than the original underlying space.
We show the importance of exploiting the complementary convex structure for efficiently solving a wide class of specially structured nonconvex global optimization problems.
The existence of coincidence points of set-valued and single-valued mappings in matric spaces and convex matric with W-convex structure is discussed. The conclusion generalizes the corresponding results in some references.