Some fixed point theorems in locally convex spaces and applications to differential and integral equations

Bogdan Rzepecki

Commentationes Mathematicae Universitatis Carolinae (1981)

  • Volume: 022, Issue: 1, page 113-127
  • ISSN: 0010-2628

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Rzepecki, Bogdan. "Some fixed point theorems in locally convex spaces and applications to differential and integral equations." Commentationes Mathematicae Universitatis Carolinae 022.1 (1981): 113-127. <http://eudml.org/doc/17090>.

@article{Rzepecki1981,
author = {Rzepecki, Bogdan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Krasnoselskij fixed point theorem; method of norm changing},
language = {eng},
number = {1},
pages = {113-127},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some fixed point theorems in locally convex spaces and applications to differential and integral equations},
url = {http://eudml.org/doc/17090},
volume = {022},
year = {1981},
}

TY - JOUR
AU - Rzepecki, Bogdan
TI - Some fixed point theorems in locally convex spaces and applications to differential and integral equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1981
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 022
IS - 1
SP - 113
EP - 127
LA - eng
KW - Krasnoselskij fixed point theorem; method of norm changing
UR - http://eudml.org/doc/17090
ER -

References

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  1. A. BIELECKI, Une remarque sur la méthode de Banach-Cacciopoli-Tikhonov dans la théorie des équations différentielles ordinaires, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 4 (1956), 261-264. (1956) MR0082073
  2. F. F. BONSALL, Lectures on some fixed point theorems of functional analysis, Tata Institute of Fundamental Research, Bombay 1962. (1962) MR0198173
  3. N. BOURBAKI, Espaces vectoriels topologiques, Paris 1953. (1953) Zbl0050.10703
  4. G. L. CAIN, Jr. M. Z. NASHED, Fixed points and stability for a sum of two operators in locally convex spaces, Pacific J. Math. 39 (1971), 581-592. (1971) MR0322606
  5. R. EDWARDS, Functional analysis, Theory and applications, New York 1965. (1965) Zbl0182.16101MR0221256
  6. C. J. HIMMELBERG:., Fixed points of compact multifunctions, J. Math. Anal. Appl. 38 (1972), 205-207. (1972) Zbl0225.54049MR0303368
  7. H. H. KELLER, Differential calculus in locally convex spaces, Springer-Verlag, Lecture Notes in Mathematics, Berlin 1974. (1974) Zbl0293.58001MR0440592
  8. M. A. KRASNOSELSKII, Two remarks on the method of succesive approximations, [in Russian], Uspehi Mat. Nauk 10 (1955), 123-127. (1955) MR0068119
  9. S. G. KREIN, Linear differential equations in a Banach space, [in Russian], Moscow 1967. (1967) MR0247239
  10. C. KURATOWSKI, Topologie v. I, Warsaw 1952. (1952) 
  11. W. R. MELVTN, Some extensions of the Krasnoselskii fixed point theorems, J. Diff. Equat. 11 (1972), 335-348. (1972) MR0301325
  12. V. MILLIONCHIKOV, A contribution to the theory of differential equations d x / d t = f ( x , t ) in locally convex space, [in Russian], DAN SSSR 131 (1960), 510-513. (1960) MR0118931
  13. M. A. NAIMARK, Normed rings, [in Russian], Moscow 1968. (1968) MR0355602
  14. M. Z. NASHED J. S. W. WONG, Some variants of a fixed point of Krasnoselskii and applications to non-linear integral equations, J. Math. Mech. 18 (1969), 767-777. (1969) MR0238140
  15. W. A. PETRYSHYN, A new fixed point theorem and its applications, Bull. Amer. Math. Soc. 2 (1972), 225-229. (1972) 
  16. D. PRZEWORSKA, ROLEWICZ, Equations with transformed argument. An algebraic approach, Warsaw 1973. (1973) Zbl0271.47008MR0493449
  17. B. RZEPECKI, On the Banach principle and its application to theory of differential equations, Comment. Math. 19 (1977), 355-363. (1977) MR0478124
  18. V. M. SEHGAL S. P. SINGH, On a fixed point theorem of Krasnoselskii for locally convex spaces, Pacific J. Math. 62 (1976), 561-567. (1976) MR0412911
  19. V. M. SEHGAL S. P. SINGH, A fixed point theorem for the sum of two mappings, Math. Japonica 23 (1978), 71-75. (1978) MR0500289
  20. K. YOSIDA, Functional analysis, Berlin 1965. (1965) Zbl0126.11504MR0180824

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