Advertisement

Results in Mathematics

, Volume 25, Issue 3–4, pp 290–314 | Cite as

Fixed Point Theorems of Krasnosel’skii Type In Locally Convex Spaces and Applications to Integral Equations

  • Le Hoan Hoa
  • Klaus Schmitt
Article

Abstract

The paper presents some fixed point theorems for operators of the form U + C on a bounded closed convex subset of a locally convex space, where C is completely continuous and Un satisfies contraction type conditions. Applications to integral equations in a Banach space are presented.

1985 Mathematics Subject Clarifiction

45G10 47H10 

En]Key words and phrases

fixed point theorems locally convex spaces integral equations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Ambrosetti, Un teorema di existenza per le equazioni differenziali sugli spazi di Banach, Rend. Sem. Math. Univ. Padua, 39 (1967), 349–361.MathSciNetGoogle Scholar
  2. 2.
    D. D. Ang and L. H. Hoa, On a fixed point theorem of Krasnosel’skii and triangle contractive operators, Fund. Math., 120 (1984), 77–98.MathSciNetMATHGoogle Scholar
  3. 3.
    D. W. Boyd and J. S. Wong, On nonlinear contractions, Proc. Amer. Math. Soc, 20 (1969), 458–464.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    F. E. Browder, A generalization of the Schauder fixed point theorem, Duke Math. J., 26 (1959), 291–303.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    F. E. Browder and R. D. Nussbaum, The topological degree for noncompact nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc, 74 (1968), 671–676.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    A Granas, The theory of compact vector fields and some of its applications to topology of functional spaces, Bull. Amer. Math. Soc, 74 (1968), 1–93.MathSciNetCrossRefGoogle Scholar
  7. 7.
    M. A. Krasnosel’skii, Two remarks on the method of successive approximation, Uspehi Math. Nauk, 10 (1955), 123–127 (in Russian).MathSciNetGoogle Scholar
  8. 8.
    S. Leader, Two convergence principles with applications to fixed points in metric space, Nonlinear Analysis, 6 (1982), 531–538.MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    A. Meir and E. Keeler, A theorem on contractive mappings, J. Math. Anal. Appl., 28 (1969), 326–329.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    M. Z. Nashed and J.S.W. Wong, Some variants of a fixed point theorem of Krasnosel’skii and applications to nonlinear integral equations, J. Math. Mechanics, 18 (1969), 767–777.MathSciNetMATHGoogle Scholar
  11. 11.
    D. H. Tan, Two fixed point theorems of Krasnosels’kii type, Rev. Roumain Math. Pure Appl. 32 (1987), 397–400.MATHGoogle Scholar
  12. 12.
    B. G. Zhang and J. S. Yu, On the existence of asymptotically decaying positive solutions of second order neutral difference equations, J. Math. Anal. Appl, 166 (1992), 1–11.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1994

Authors and Affiliations

  • Le Hoan Hoa
    • 1
  • Klaus Schmitt
    • 2
  1. 1.Dai Hock SuPhan-School of EducationHoChiMinh CityVietnam
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityUSA

Personalised recommendations