GFC-度量空间中的GR-KKM定理及其对极大元的应用
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摘要
本文引入GFC-度量空间,建立GFC-度量空间中GR-KKM定理.作为应用,在非紧框架下,得到GFC-度量空间的相交点集、Ky Fan截口和极大元集为非空紧集.
In this paper, GFC-metric spaces are introduced and a GR-KKM theorem is established in GFC-metric spaces. As applications, in noncompact settings, we obtain that intersection point sets, Ky Fan sections and maximal element sets are nonempty and compact in GFC-metric spaces.
In this paper, GFC-metric spaces are introduced and a GR-KKM theorem is established in GFC-metric spaces. As applications, in noncompact settings, we obtain that intersection point sets, Ky Fan sections and maximal element sets are nonempty and compact in GFC-metric spaces.
引文
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[4]DING Xieping,XIA Fuquan.Generalized H-KKM type theorems in H-metric spaces with application[J].Appl.Math.Mech.(English Edition),2001,22(10):1140-1148.
[5]孟莉、沈自飞、程小力.G-凸度量空间中的KKM定理及其应用[J].应用泛函分析学报,2005,7(3):273-279.
[6]WEN Kaiting.A Ky Fan matching theorem in complete L-convex metric spaces and its application to abstract economies[J].Math.Appl.,2007,20(3):593-597.
[7]文开庭.FC-度量空间中的R-KKM定理及其对抽象经济的应用[J].西南师范大学学报(自然科学版),2010,35(1):45-49.
[8]KHANH P Q,QUAN N H,YAO J C.Generalized KKM-type theorems in GFC-spaces and applications[J].Nonlinear Anal.,2009,71(3-4):1227-1234.
[9]WEN Kaiting.A GFs-KKM theorem in GFC-spaces and the application to coincidence problems[J].Math.Appl.,2015,28(3):533-539.
[10]WEN Kaiting.GLKKM theorems in L-convex metric spaces with application[J].Acta Anal.Funct.Appl.,2008,10(2):109-115.
[11]文开庭.FC-度量空间中的R-KKM定理及其对变分不等式和不动点的应用[J].应用泛函分析学报,2010,12(3):266-273.
[12]WEN Kaiting.A GLKKM type theorem for noncompact complete L-convex metric spaces with applications to variational inequalities and fixed points[J].J.Math.Res.Exposition,2009,29(1):19-27.
[13]文开庭.非紧超凸度量空间中的Browder不动点定理及其对重合问题的应用[J].数学进展,2005,34(2):208-212.
[14]CHEN Fengjuan,SHEN Zifei.Continuous selection theorem and coincidence theorem on hyperconvex spaces[J].Adv.Math.China,2005,34(5):614-618.
[2]KHAMSI M A.KKM and Ky Fan theorems in hyperconvex metric spaces[J].J.Math.Anal.Appl.,1996,204:298-306.
[3]KIRK W A,SIMS B,YUAN X Z.The Knaster-Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications[J].Nonlinear Anal.,2000,39:611-627.
[4]DING Xieping,XIA Fuquan.Generalized H-KKM type theorems in H-metric spaces with application[J].Appl.Math.Mech.(English Edition),2001,22(10):1140-1148.
[5]孟莉、沈自飞、程小力.G-凸度量空间中的KKM定理及其应用[J].应用泛函分析学报,2005,7(3):273-279.
[6]WEN Kaiting.A Ky Fan matching theorem in complete L-convex metric spaces and its application to abstract economies[J].Math.Appl.,2007,20(3):593-597.
[7]文开庭.FC-度量空间中的R-KKM定理及其对抽象经济的应用[J].西南师范大学学报(自然科学版),2010,35(1):45-49.
[8]KHANH P Q,QUAN N H,YAO J C.Generalized KKM-type theorems in GFC-spaces and applications[J].Nonlinear Anal.,2009,71(3-4):1227-1234.
[9]WEN Kaiting.A GFs-KKM theorem in GFC-spaces and the application to coincidence problems[J].Math.Appl.,2015,28(3):533-539.
[10]WEN Kaiting.GLKKM theorems in L-convex metric spaces with application[J].Acta Anal.Funct.Appl.,2008,10(2):109-115.
[11]文开庭.FC-度量空间中的R-KKM定理及其对变分不等式和不动点的应用[J].应用泛函分析学报,2010,12(3):266-273.
[12]WEN Kaiting.A GLKKM type theorem for noncompact complete L-convex metric spaces with applications to variational inequalities and fixed points[J].J.Math.Res.Exposition,2009,29(1):19-27.
[13]文开庭.非紧超凸度量空间中的Browder不动点定理及其对重合问题的应用[J].数学进展,2005,34(2):208-212.
[14]CHEN Fengjuan,SHEN Zifei.Continuous selection theorem and coincidence theorem on hyperconvex spaces[J].Adv.Math.China,2005,34(5):614-618.