Weak and strong topologies and integral equations in Banach spaces

Donal O'Regan

Annales Polonici Mathematici (1995)

  • Volume: 61, Issue: 3, page 245-260
  • ISSN: 0066-2216

Abstract

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The Schauder-Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel’skiĭ’s fixed point theorem due to Nashed and Wong are used to establish existence of L α and C solutions to Volterra and Hammerstein integral equations in Banach spaces.

How to cite

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Donal O'Regan. "Weak and strong topologies and integral equations in Banach spaces." Annales Polonici Mathematici 61.3 (1995): 245-260. <http://eudml.org/doc/262401>.

@article{DonalORegan1995,
abstract = {The Schauder-Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel’skiĭ’s fixed point theorem due to Nashed and Wong are used to establish existence of $L^α$ and C solutions to Volterra and Hammerstein integral equations in Banach spaces.},
author = {Donal O'Regan},
journal = {Annales Polonici Mathematici},
keywords = {Volterra; Hammerstein; existence; integral equations in abstract spaces; weak and strong topologies; Volterra integral equation; Hammerstein integral equation; Banach space; Schauder-Tikhonov fixed point theorem; Krasnosel'skij's fixed point theorem},
language = {eng},
number = {3},
pages = {245-260},
title = {Weak and strong topologies and integral equations in Banach spaces},
url = {http://eudml.org/doc/262401},
volume = {61},
year = {1995},
}

TY - JOUR
AU - Donal O'Regan
TI - Weak and strong topologies and integral equations in Banach spaces
JO - Annales Polonici Mathematici
PY - 1995
VL - 61
IS - 3
SP - 245
EP - 260
AB - The Schauder-Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel’skiĭ’s fixed point theorem due to Nashed and Wong are used to establish existence of $L^α$ and C solutions to Volterra and Hammerstein integral equations in Banach spaces.
LA - eng
KW - Volterra; Hammerstein; existence; integral equations in abstract spaces; weak and strong topologies; Volterra integral equation; Hammerstein integral equation; Banach space; Schauder-Tikhonov fixed point theorem; Krasnosel'skij's fixed point theorem
UR - http://eudml.org/doc/262401
ER -

References

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  2. [2] J. K. Brooks and N. Dinculeanu, Weak compactness in spaces of Bochner integrable functions and applications, Adv. in Math. 24 (1977), 172-188. Zbl0354.46026
  3. [3] C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973. 
  4. [4] C. Corduneanu, Integral Equations and Applications, Cambridge Univ. Press, New York, 1990. 
  5. [5] C. Corduneanu, Perturbations of linear abstract Volterra equations, J. Integral Equations Appl. 2 (1990), 393-401. 
  6. [6] C. Corduneanu, Abstract Volterra equations and weak topologies, in: Delay Differential Equations and Dynamical Systems, S. Busenberg and M. Martelli (eds.), Lecture Notes in Math. 1475, Springer, 110-116. 
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  10. [10] J. Dugundji and A. Granas, Fixed Point Theory, Monograf. Mat. 61, PWN, Warszawa, 1982. 
  11. [11] N. Dunford and J. T. Schwartz, Linear Operators, Interscience Publ. Inc., Wiley, New York, 1958. 
  12. [12] C. F. Dunkl and K. S. Williams, A simple norm inequality, Amer. Math. Monthly 71 (1964), 53-54. 
  13. [13] G. Gripenberg, S. O. Londen and O. Staffans, Volterra Integral and Functional Equations, Cambridge Univ. Press, New York, 1990. Zbl0695.45002
  14. [14] R. B. Guenther and J. W. Lee, Some existence results for nonlinear integral equations via topological transversality, J. Integral Equations Appl. 5 (1993), 195-209. Zbl0781.45003
  15. [15] R. H. Martin, Jr., Nonlinear Operators and Differential Equations in Banach Spaces, Wiley, New York, 1976. 
  16. [16] M. Z. Nashed and J. S. W. Wong, Some variants of a fixed point theorem of Krasnosel'skiĭ and applications to nonlinear integral equations, J. Math. Mech. 18 (1969), 767-777. Zbl0181.42301
  17. [17] K. Yosida, Functional Analysis, Springer, Berlin, 1971. 

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