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1995 | 61 | 3 | 245-260
Tytuł artykułu

Weak and strong topologies and integral equations in Banach spaces

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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.
Twórcy
  • Department of Mathematics, University College Galway, Galway, Ireland
Bibliografia
  • [1] D. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464.
  • [2] J. K. Brooks and N. Dinculeanu, Weak compactness in spaces of Bochner integrable functions and applications, Adv. in Math. 24 (1977), 172-188.
  • [3] C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973.
  • [4] C. Corduneanu, Integral Equations and Applications, Cambridge Univ. Press, New York, 1990.
  • [5] C. Corduneanu, Perturbations of linear abstract Volterra equations, J. Integral Equations Appl. 2 (1990), 393-401.
  • [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.
  • [7] J. B. Conway, A Course in Functional Analysis, Springer, Berlin, 1990.
  • [8] D. G. DeFigueiredo and L. A. Karlovitz, On the radial projection in normed spaces, Bull. Amer. Math. Soc. 73 (1967), 364-368.
  • [9] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, 1977.
  • [10] J. Dugundji and A. Granas, Fixed Point Theory, Monograf. Mat. 61, PWN, Warszawa, 1982.
  • [11] N. Dunford and J. T. Schwartz, Linear Operators, Interscience Publ. Inc., Wiley, New York, 1958.
  • [12] C. F. Dunkl and K. S. Williams, A simple norm inequality, Amer. Math. Monthly 71 (1964), 53-54.
  • [13] G. Gripenberg, S. O. Londen and O. Staffans, Volterra Integral and Functional Equations, Cambridge Univ. Press, New York, 1990.
  • [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.
  • [15] R. H. Martin, Jr., Nonlinear Operators and Differential Equations in Banach Spaces, Wiley, New York, 1976.
  • [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.
  • [17] K. Yosida, Functional Analysis, Springer, Berlin, 1971.
Typ dokumentu
Bibliografia
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