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NEW FIXED POINT THEOREMS FOR P_1-COMPACT MAPPINGS IN BANACH SPACES

NEW FIXED POINT THEOREMS FOR P_1-COMPACT MAPPINGS IN BANACH SPACES
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摘要 E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc. E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.
作者 Shaoyuan Xu
机构地区 Department of Mathematics Huaibei Colal Industry Teachers College Huaibei
出处 《Analysis in Theory and Applications》 2007年第3期274-282,共9页 分析理论与应用（英文刊）
基金 Supported in part by Education Ministry,Anhui Province,China(No:2003kj047zd)
关键词 A-proper mapping P1-compact mapping completely continuous operator topological degree fixed point theorem A-proper mapping, P1-compact mapping, completely continuous operator,topological degree, fixed point theorem
分类号 O177.2 [理学—基础数学]
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参考文献11

  • 1王元恒,沈自飞.Banach空间中的广义Schauder基和广义A-proper映射的广义拓扑度[J].数学年刊（A辑）,2003,24(5):531-540. 被引量：2
  • 2Petryshyn,W.V.On a Approximation Solvability of Equations Involving A-Proper and Pseudo-A-Proper Mappings[].Bulletin of the American Mathematical Society.1975
  • 3Petryshyn,W.V.On a Fixed Point Theorem for Nonlinear P-Compact Operators in Banach Spaces[].Bull AmerMathSoe.1966
  • 4Petryshyn,W.V.On Nonlinear P-Compact Operators in Banach Spaces with Approximations to Constructive Fixed Point Theorems[].Journal of Mathematical Analysis and Applications.1966
  • 5Zeidler,E.Nonlinear Functional Analysis and its Applications[]..1986
  • 6Granas,A,Dugundji,J.Fixed Point Theory[]..2003
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  • 8W. V. Petryshyn&#x00.Bifurcation and asymptotic bifurcation for equations involving A-proper mappings with applications to differential equations[].Journal of Differential Equations.1978
  • 9WANG Yuanheng SHEN ZifeiDepartment of Mathematics,Zhejiang Normal University,Jinhua 321004,Zhejiang,China.GENERALIZED SCHAUDER BASES AND THE GENERALIZED TOPOLOGICAL DEGREEFOR GENERALIZED A-PROPER MAPPINGS IN BANACH SPACES[].Chinese Annals of Mathematicsseries A.2003
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二级参考文献14

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共引文献1

Analysis in Theory and Applications
2007年 第3期

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