In this paper,the Knaster-Karatowski-Mazurkiewicz technique(KKM technique,in short)is presented.By using this technique a new alternative theorem and a new coincidence theorem are established.The results obtained in t...In this paper,the Knaster-Karatowski-Mazurkiewicz technique(KKM technique,in short)is presented.By using this technique a new alternative theorem and a new coincidence theorem are established.The results obtained in this paper unify and generalize the corresponding results in the recent works.展开更多
Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems co...Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems concerning maximal elements, analytic alternatives and minimax inequalities.展开更多
In this paper, two alternative theorems which differ from Theorem 10.2.6 in [1] and Theorem 1 in [3] are presented for a class of feasible direction algorithms. On the basis of alternative theorems, furthermore, two s...In this paper, two alternative theorems which differ from Theorem 10.2.6 in [1] and Theorem 1 in [3] are presented for a class of feasible direction algorithms. On the basis of alternative theorems, furthermore, two sufficient conditions of global convergence of this class of algorithms are obtained.展开更多
In this paper, the theorem of the alternative based on separation functions in ordered locally convex topological vector spaces has been established by using the concept on set valued mappings. The optimality con...In this paper, the theorem of the alternative based on separation functions in ordered locally convex topological vector spaces has been established by using the concept on set valued mappings. The optimality conditions in ref. for D convex function have been generalized to ordered locally convex topological vector space and the similarly optimality conditions for D subconvexlike functions, such as the necessary and sufficient conditions of nondominated solutions, the generalized saddle point theorems and the lagrange duality theorems, have been obtained.展开更多
文摘In this paper,the Knaster-Karatowski-Mazurkiewicz technique(KKM technique,in short)is presented.By using this technique a new alternative theorem and a new coincidence theorem are established.The results obtained in this paper unify and generalize the corresponding results in the recent works.
文摘Using a fixed point theorem by Kuo, Jeng and Huang, we obtain in G-convex spaces a very general intersection theorem concerning the values of three maps. From this result we derive successively alternative theorems concerning maximal elements, analytic alternatives and minimax inequalities.
文摘In this paper, two alternative theorems which differ from Theorem 10.2.6 in [1] and Theorem 1 in [3] are presented for a class of feasible direction algorithms. On the basis of alternative theorems, furthermore, two sufficient conditions of global convergence of this class of algorithms are obtained.
文摘In this paper, the theorem of the alternative based on separation functions in ordered locally convex topological vector spaces has been established by using the concept on set valued mappings. The optimality conditions in ref. for D convex function have been generalized to ordered locally convex topological vector space and the similarly optimality conditions for D subconvexlike functions, such as the necessary and sufficient conditions of nondominated solutions, the generalized saddle point theorems and the lagrange duality theorems, have been obtained.
