Hausdorff局部凸空间内集值终归紧映象的不动点指数及其应用<sup>*</sup>

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Hausdorff局部凸空间内集值终归紧映象的不动点指数及其应用^*

基金项目: 中国科学院科学基金资助的课题

摘要: 在本文内我们对Hausdorff局部凸拓扑矢量空间内的集值终归紧映象定义了不动点指数概念,利用此概念,我们证明了集值φ-凝聚映象的几个非零不动点定理,这些定理推广了[1,2,7,8,9]中的某些已知结果。

Abstract: The author defines a concept of fixed point index of ultimately compact set-valued mappings in Hausdorff locally convex spaces. Using this concept, the author establishes several nonzero fixed point theorems of set-valued Φ-condensing mappings. These theorems extend some known results in [1,2,7,8,9].

[1]	Fizpatrick, P.M.and W.V.Petryshyn, Fixed point theorems and the fixed point index for multivalued mappings in cones, J London Math.Soc., 12 (1975), 75-85.
[2]	Petryshyn, W.V.and P.M.Fizpatrick, A degree theory, fixed point theroems, and mapping theorem for multivalued noncompact mappings, Trans.Amer.Math.Soc., 194 (1974), 1-25.
[3]	Duc, D.M.D.D.Thanh and D.D.Ang, Relative topological degree of set-valued compact vector fields and its applications, J.Math.Anal.appl., 80 (1981), 406-432.
[4]	Sadovskii, B.N., Measures of noncompactness and condensing operators, Prob.Mat.Anal.Sloz Sistem, 2(1968), 89-119.
[5]	Schaefer, H.H., Topological Vector Spaces, Springer-Verlag, New York, Fourth, Corrected Printing (1980).
[6]	Ma, T.W., Topological degrees for set-valued compact vector fields in locally convex spaces, Dissertationes Math., 92 (1972), 1-43.
[7]	郭大钧,关于锥映象的几个不动点定理,科学通报,28, 20 (1983),1217-1219
[8]	Gatica, J.A.and H.L.Smith, Fixed point techniques in cone with applications, J.Math.Anal.Appl., 61(1977), 58-71.
[9]	Leggett, R.W.and L.A.Williams, A fixed point theorem with application to an infectious disease model, J.Math.Anal.Appl., 76 (1980), 91-97．