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Solutions with big graph of the equation of invariant curves

Języki publikacji
EN
Abstrakty
EN
We consider the functional equation of invariant curves [phi(f(x, phi(x))) = g(x, phi(x))] and we look for its solution which has a big graph. Such a graph is big from the point of view of topology and measure theory.
Rocznik
Strony
309--317
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
  • Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Bibliografia
  • [1] L. Bartłomiejczyk, Solutions with big graph of homogeneous functional equations, Aequationes Math., 56 (1998) 149-156.
  • [2] L. Bartłomiejczyk, Solutions with big graph of iterative functional equations of the first order, Colloq. Math., 82 (1999) 223-230.
  • [3] L. Bartłomiejczyk, Solutions with big graph of an equation of the second iteration, Aequationes Math., to be published.
  • [4] L. Bartłomiejczyk, Iterative roots with big graph, Real Anal. Exchange, to be published.
  • [5] J. P. R.. Christensen, On sets of Haar measure zero in abelian Polish groups, Israel J. Math., 13 (1972) 255-260.
  • [6] J. P. R. Christensen, Topology and Borel structure, North-Holland Math. Stud., 10, North-Holland Publishing Company and American Elsevier Publishing Company, Amsterdam-London-New York 1974.
  • [7] R. Engelking, General topology, Monografie Matematyczne, 60, PWN-Polish Scientific Publishers, Warszawa 1977.
  • [8] P. R.. Halmos, Measure Theory, Grad. Texts in Math. 18, Springer-Verlag, New York-Heidleberg-Berlin 1974.
  • [9] F. B. Jones, Connected and disconnected plane sets and the functional equation ,f (x) + f (y) = f (x + y), Bull. Amer. Math. Soc., 48 (1942) 115-120.
  • [10] P. Kahlig„1. Smital, On the solutions of a functional equation of .Dhorn-byes, Results Math., 27 (1995) 362-367.
  • [11] M. Kuczma, Functional equations in a single variable, Monografie Matematyczne, 46, PWN-Polish Scientific. Publishers, Warszawa 1968.
  • [12] M. Kuczma, An introduction to the theory of functional equations and inequalities. Cauchy's equation and Jensen's inequality, Prace Naukowe Uniwersytetu Śląskiego w Katowicach, 489, Państwowe Wydawnictwo Naukowe mid Uniwersytet Śląski, Warszawa-Kraków-Katowice 1985.
  • [13] M. Kuczma, B. Choczewski, R. Ger, Iterative functional equations, Encyclopedia Math. App. 32, Cambridge University Press, Cambridge-New York-Port Chester-Melbourne-Sydney 1990.
  • [14] K. Kuratowski, A. Mostowski, Set theory, Stud. Logic Found. Math., 86, PWN-Polish Scientific Publishers and North-Holland Publishing Company, Warszawa-Amsterdam-New York-Oxford 1976.
  • [15] J. Morawiec, On the existence of irregular solutions of the two-coefficient dilation equation, Aequationes Math., to be published.
  • [16] J. C. Oxtoby, Measure and category, Grad. Text in Math., 2, Springer-Verlag, New York-Heidleberg-Berlin 1971.
  • [17] K. R. Parthasarathy, Probability measures on metric spaces, Academic Press, New York-San Francisco-London 1967.
  • [18] J. Smítal, On Darboux solutions of the. Euler's equation, Aequationes Math., 37 (1989) 279-281.
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT2-0001-1615