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1998 | 131 | 2 | 143-148
Tytuł artykułu

Asymptotic stability in the Schauder fixed point theorem

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EN
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EN
This note presents a theorem which gives an answer to a conjecture which appears in the book Matrix Norms and Their Applications by Belitskiĭ and Lyubich and concerns the global asymptotic stability in the Schauder fixed point theorem. This is followed by a theorem which states a necessary and sufficient condition for the iterates of a holomorphic function with a fixed point to converge pointwise to this point.
Czasopismo
Rocznik
Tom
131
Numer
2
Strony
143-148
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-04-16
poprawiono
1998-04-04
Twórcy
autor
  • Department of Mathematics, Chung Yuan University, Chung-Li, Taiwan 320
Bibliografia
  • [1] G. R. Belitskiĭ and Yu. I. Lyubich, Matrix Norms and Their Applications, translated from the Russian by A. Iacob, Birkhäuser, 1988.
  • [2] M. S. Berger, Nonlinearity and Functional Analysis, Academic Press, 1977.
  • [3] J. Dugundji, Topology, Allyn and Bacon, 1969.
  • [4] H. Federer, Geometric Measure Theory, Springer, Berlin, 1969.
  • [5] T. Franzoni and E. Vesentini, Holomorphic Maps and Invariant Distances, North-Holland, 1980.
  • [6] L. A. Harris, Schwarz's lemma in normed linear spaces, Proc. Nat. Acad. Sci. U.S.A. 62 (1969), 1014-1017.
  • [7] R. B. Holmes, A formula for the spectral radius of an operator, Amer. Math. Monthly 75 (1968), 163-166.
  • [8] R. B. Kellogg, Uniqueness in the Schauder fixed point theorem, Proc. Amer. Math. Soc. 60 (1976), 207-210.
  • [9] V. Khatskevich and D. Shoiykhet, Differentiable Operators and Nonlinear Equations, Oper. Theory Adv. Appl. 66, Birkhäuser, 1994.
  • [10] J. Kitchen, Concerning the convergence of iterates to fixed points, Studia Math. 27 (1966), 247-249.
  • [11] Yu. I. Lyubich, A remark on the stability of complex dynamical systems, Izv. Vyssh. Uchebn. Zaved. Mat. 10 (1983), 49-50 (in Russian); English transl.: Soviet Math. (Iz. VUZ) 10 (1983), 62-64.
  • [12] W. Rudin, Function Theory in the Unit Ball of $ℂ^n$, Springer, 1980.
  • [13] J. Schauder, Der Fixpunktsatz in Funktionalräumen, Studia Math. 2 (1930), 171-180.
  • [14] J. T. Schwartz, Nonlinear Functional Analysis, Courant Inst. Math. Sci., New York Univ., 1964.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv131i2p143bwm
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