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On the problem of dissipative perturbations of nonexpansive mappings

  • Luo Yuan-song
Article
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Abstract

Some fixed point theorems for mappings of the type — A+T are established, where P is a cone in a Hilbert space,A:P→2P is an accretive mappings andT:P→P is a nonexpansive mappings. In application, the results presented in the paper are used to study the existence problem of solutions for a class of nonlinear integral equations in L2(Ω).

Key words

nonexpansive mapping accretive mapping fixed point theorem nonlinear integral equation 

CLC number

O177.91 

References

  1. [1]
    Gatica J A, Kirk W A. Fixed point theorems for contraction mappings with applications to nonexpansive and pseudo-contractive mappings[J].Rocky Mountain J Math, 1994,4:69–79.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Kirk W A, Schonberg R. Some results on pseudo-contractive mappings[J].Pacific J Math, 1977,71:89–100.zbMATHMathSciNetGoogle Scholar
  3. [3]
    Morales C. Pseudo-contractive mappings and the Leray-Schauder boundary condition[J].Comment Math Univ Carolinae, 1979,20:745–756.zbMATHMathSciNetGoogle Scholar
  4. [4]
    Reinermann J, Schonberg R.Some Results and Problems in the Fixed Point Theory for Nonexpansive and Pseudo-Contractive Mappings in Hilbert Spaces[M]. S Swaminathaned: Academic Press, 1976.Google Scholar
  5. [5]
    Chen Y Q. The fixed point index for accretive mappings withk-set contraction perturbation in cones [J].Internat J Math Math Sci, 1996,19(2):287–290.zbMATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Chen Y Q. On accretive operators in cones of Banach spaces[J].Nonlinear Anal, TMA, 1996,27 (10): 1125–1135.zbMATHCrossRefGoogle Scholar
  7. [7]
    Chen Y Q, Cho Y J. On 1-set contractions accretive operators in cones of Banach spaces[J].J Math Anal Appl, 1996,201(3): 966–980.zbMATHMathSciNetCrossRefGoogle Scholar
  8. [8]
    Alspach D E: A fixed point free nonexpansive map[J].Proc Amer Math Soc, 1981,82(3): 423–424.zbMATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    Browder F E. Nonlinear nonexpansive operators in Banach spaces[J].Proc Nat Acad Sci USA, 1965,54: 1041–1044.zbMATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    Browder F E. Nonlinear operators and nonlinear equations of evolution in Banach spaces[J].Proc Sympos Pure Math, 1976,18(2):1023–1027.MathSciNetGoogle Scholar
  11. [11]
    ZHANG Shi-sheng.Fixed Point Theory With Applications[M]. Chongqing: Chongqing Press, 1984. (in Chinese)Google Scholar
  12. [12]
    Isac G. On an Altman type fixed point theorem on convex cones[J].Rocky Mountain J Math, 1995,2: 701–714.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Luo Yuan-song
    • 1
  1. 1.Department of MathematicsYibin Teachers' CollegeYibinP R China

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