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KKM and KY fan theorems in modular function spaces
Khamsi Mohamed,Latif Abdul,Al-Sulami Hamid
Fixed Point Theory and Applications , 2011,
Abstract: In modular function spaces, we introduce Knaster-Kuratowski-Mazurkiewicz mappings (in short KKM-mappings) and prove an analogue to Ky Fan s fixed point theorem. 2010 Mathematics Subject Classification: Primary 46B20, 47H09; Secondary 47H10.
A GENERALIZATION OF FKKM-TYPE THEOREM WITH APPLICATIONS
FKKM-型定理的推广及应用
Shi Sheng ZHANG,
张石生
系统科学与数学 , 1999,
Abstract: in this paper some new generalizations of FKKM type theorem are given.As applications, we utilize these results to study the coincidence point problem. The resultspresented in this paper unify and contain some recede results of the authors.
Some new deterministic and random variational inequalities and their applications
Xian-Zhi Yuan,Jean-Marc Roy
International Journal of Stochastic Analysis , 1995, DOI: 10.1155/s1048953395000347
Abstract: A non-compact deterministic variational inequality which is used to prove an existence theorem for saddle points in the setting of topological vector spaces and a random variational inequality. The latter result is then applied to obtain the random version of the Fan's best approximation theorem. Several random fixed point theorems are obtained as applications of the random best approximation theorem.
A study of variational inequalities for set-valued mappings
Tan Kok-Keong,Tarafdar Enayet,Yuan George Xian-Zhi
Journal of Inequalities and Applications , 1999,
Abstract: In this paper, Ky Fan's KKM mapping principle is used to establish the existence of solutions for simultaneous variational inequalities. By applying our earlier results together with Fan–Glicksberg fixed point theorem, we prove some existence results for implicit variational inequalities and implicit quasi-variational inequalities for set-valued mappings which are either monotone or upper semi-continuous.
On the generalized vector F-implicit complementarity problems and vector F-implicit variational inequality problems
Amini-Harandi, A.,Farajzadeh, A. P.,Noor, M. A.
- , 2007,
Abstract: Sa？etak In this paper, we introduce and analyze some new classes of generalized vector-F implicit complementarity problems and the general mixed vector-F variational inequalities. Under suitable conditions, we prove the equivalences between these new problems. We establish several existence theorems for these classes of vector-F complementarity and general mixed vector-F variational inequalities using a new version of the Fan-KKM theorem in Hausdorff topological vector spaces, and without even using the classical assumptions in this context, like monotonicity or continuity. Results obtained in this paper represent significant improvement and refinement of the previously known results
对称算子均衡问题解的存在性分析
Existence analysis of solutions for symmetric operator equilibrium problems
张卫兵,颜文勇
- , 2017,
Abstract: 本文主要研究了拓扑向量空间中对称算子均衡问题解的存在性. 在自然拟 -凸及 -上半连续的条件下，利用KKMF定理获得了拓扑向量空间中对称算子均衡问题解的存在性定理. 我们的结果改进和推广了现有的工作.
In this paper, the existence of solutions for symmetric operator equilibrium problems is investigated in topological vector spaces. By virtue of the conditions of natural quasi-C-convex and C-upper semicontinuity , using the KKM Theorem, the existence theorems of solutions for symmetric operator equilibrium problems are obtained. Our results improve and extent the corresponding results that have studied
GFC度量空间中的GR-KKM定理及其对重合问题的应用
A GR-KKM Theorem in GFC-Metric Spaces and Its Application to Coincidence Problems
文开庭
- , 2017, DOI: 10.13718/j.cnki.xdzk.2017.11.009
Abstract: 引入了GFC-度量空间，建立了GFC-度量空间中的GR-KKM定理.作为应用，在非紧框架下得到GFC-度量空间中的极大元集、变分不等式解集和重合点集为非空紧集.
In this paper, the GFC-metric space is introduced and a GR-KKM theorem in it is established. As applications, in noncompact settings, we obtain that maximal element sets, solution sets of variational inequalities and coincidence sets in GFC-metric spaces are nonempty and compact
一类向量变分不等式解的存在性研究
Existence of Solutions for a Class of Vector Variational Inequalities  [PDF]
张琦霞
Pure Mathematics (PM) , 2025, DOI: 10.12677/pm.2025.158217
Abstract: 向量变分不等式作为重要的数学工具，在交通、能源与资源调度等领域中具有广泛应用。本文针对一类有限维空间上的经典向量变分不等式，借助KKM原理证明了在不同条件下其解的存在性，并将该模型应用于城市地铁多线路调度优化问题。
The vector variational inequality, as an important mathematical tool, has found wide applications in fields such as transportation, energy, and resource scheduling. This paper investigates a class of classical vector variational inequalities defined in finite-dimensional spaces. By employing the KKM principle, we establish the existence of solutions under various conditions. Furthermore, we apply the proposed model to optimize the scheduling of multiple lines in an urban subway system.
集支付函数的向量均衡问题存在性定理
Existence Theorems of Vector Equilibrium Problems with Set Payoffs Functions  [PDF]
高磊, 张宇, 曹志娟
Pure Mathematics (PM) , 2020, DOI: 10.12677/PM.2020.104037
Abstract:
基于集支付函数锥半连续和锥拟凸的定义，利用经典的Fan-KKM定理与分离定理，在新的假设条件下，得到了带有集支付函数的向量均衡问题解的存在性定理。最后，通过算例验证了结果的可行性。
Based on the definitions of cone semicontinuous and cone quasiconvex of payoff function, the existence theorems of solutions for vector equilibrium problems with payoff function are obtained under new assumptions by using the classical Fan-KKM theorem and separation theorem. Finally, the feasibility of the results is verified by an example.
A general vector-valued variational inequality and its fuzzy extension
Sehie Park,Byung-Soo Lee,Gue Myung Lee
International Journal of Mathematics and Mathematical Sciences , 1998, DOI: 10.1155/s0161171298000891
Abstract: A general vector-valued variational inequality (GVVI) is considered. We establish the existence theorem for (GVVI) in the noncompact setting, which is a noncompact generalization of the existence theorem for (GVVI) obtained by Lee et al., by using the generalized form of KKM theorem due to Park. Moreover, we obtain the fuzzy extension of our existence theorem.
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