| EQUILIBRIUM PROBLEMS WITH LOWER AND UPPER BOUNDS IN TOPOLOGICAL SPACES |
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| 作者姓名： | 丁协平 |
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| 作者单位： | College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China |
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| 摘 要： | 1IntroductionLet X be a topological space and f:X×X→R{±∞}be a function.The equilibriumproblem(EP(X,f))is to find x?∈X such thatf(x?,y)≥0,?y∈X.(1)The EP(X,f)(1)includes many fundamental mathematical problems that arise from mechan-ics,engineering,economics,optimization,fixed point,saddle point,variational inequality andcomplementarity problem as special cases.See,for example,1-4].In1999,Isac,Sehgal and Singh5]raised the following open problem:given a nonemptyclosed subset K in a…
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| 关 键 词： | 平衡问题 定点理论 收缩空间 非循环空间 拓扑空间 |
| 收稿时间： | 2003-03-17 |
EQUILIBRIUM PROBLEMS WITH LOWER AND UPPER BOUNDS IN TOPOLOGICAL SPACES |
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| Ding Xieping.EQUILIBRIUM PROBLEMS WITH LOWER AND UPPER BOUNDS IN TOPOLOGICAL SPACES[J].Acta Mathematica Scientia,2005,25(4):658-662. |
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| Authors: | Ding Xieping |
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| Institution: | 1. Instituto de Inv. para la Gestión Integrada de Zonas Costeras - IGIC, Escuela Politécnica Superior de Gandia, Universitat Politècnica de València, Paranimf, 1, 46730, Grau de Gandia, Spain;2. Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, Carretera de Valldemossa km. 7.5, 07122, Palma, Spain;1. School of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, PR China;2. Guangxi Center for Mathematical Research, Guangxi University, Nanning, Guangxi 530004, PR China;3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China;4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China;1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;2. IECL UMR 7502, University of Lorraine, B.P. 70239, F-54506 Vandoeuvre-lès-Nancy Cedex, France |
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| Abstract: | By employing a fixed point theorem due to Ding, Park and Jung, some existence theorems of solutions for equilibrium problems with lower and upper bounds are proved in noncompact topological spaces. These results further answer the open problem raised by Isac, Sehgal and Singh under much weaker assumptions. |
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| Keywords: | Equilibrium problem fixed point theorem contractible space acyclic space topological space |
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