集值严格集-压缩映象的一致极限的不动点指数及其应用
Fixed Point Index of Uniform Limit of Set-Valued Strict Set-Contractive Mappings and Its Applications
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摘要: 在本文中,我们研究了一类集值严格集-压缩映象的一致极限映象.建立了这类一致极限映象的不动点指数理论,证明了某些正不动点定理.我们的定理推广了Fitzpatrick和Petryshyn的某些最近结果.Abstract: In this paper, the class of uniform limit mappings of set-valued, strick set-contractive mappings is discussed.Furthermore, the fixed point index theory for the uniform limit mappings is established.Using the fixed point index theory, some positive fixed point theorems are proved.Our theorems generalize some results in [1,4,5,7].
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Key words:
- fixed point index /
- fixed point theorem /
- subjectivity theorem
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[1] Fitzpatrick,P.M.and W.V.Petryshyn,Fixed point theorems and the fixed point index for multivalued mappings in cones,J.London Math.Soc.,12,2(1975),75-85. [2] Petryshyn,W.V.,Some results on multiple positive fixed points of multivalued condensing mappings,Contemporary Math.,21(1983),171-177. [3] Petryshyn,W.V.,Multiple positive fixed points of multivalued condensing mappings with some applications,J.Math.Anal.Appl.,124(1987),237-253. [4] Petryshyn,W.V.,Fixed point theorems for various classes of 1-set-contraction and 1-ball-contractive mappings in Banach spaces,Trans.Am.Math.Soc.,182(1973).323-352. [5] Petryshyn,W.V.and P.M.Fitzpatrick,A degree theory,fixed point theorems,mapping theorems for multivalued noncompact mappings,Trans.Am.Math.Soc.,194(1974),1-25. [6] Castaing,C.and M.Valadier,Convex Analysis and Measurable Multifunctions,Lecture Notes in Math.,580,New York(1977). [7] Zhang Qing-yong,Subjectivity for multivalued 1-φ-contractive fields,Kexue Tongbao,31,24(1986). -
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