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1999 | 82 | 2 | 223-230
Tytuł artykułu

Solutions with big graph of iterative functional equations of the first order

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We obtain a result on the existence of a solution with big graph of functional equations of the form g(x,𝜑(x),𝜑(f(x)))=0 and we show that it is applicable to some important equations, both linear and nonlinear, including those of Abel, Böttcher and Schröder. The graph of such a solution 𝜑 has some strange properties: it is dense and connected, has full outer measure and is topologically big.
Słowa kluczowe
Rocznik
Tom
82
Numer
2
Strony
223-230
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-08-27
poprawiono
1999-07-01
Twórcy
  • Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Bibliografia
  • [1] L. Bartłomiejczyk, Solutions with big graph of homogeneous functional equations in a single variable, Aequationes Math. 56 (1998), 149-156.
  • [2] L. Bartłomiejczyk, Solutions with big graph of the equation of invariant curves, submitted.
  • [3] L. Bartłomiejczyk, Iterative roots with big graph, submitted.
  • [4] L. Bartłomiejczyk, Solutions with big graph of an equation of the second iteration, submitted.
  • [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, Amsterdam, 1974.
  • [7] P. R. Halmos, Measure Theory, Grad. Texts in Math. 18, Springer, New York, 1974.
  • [8] 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.
  • [9] P. Kahlig and J. Smítal, On the solutions of a functional equation of Dhombres, Results Math. 27 (1995), 362-367.
  • [10] M. Kuczma, Functional Equations in a Single Variable, Monografie Mat. 46, PWN-Polish Sci. Publ., Warszawa, 1968.
  • [11] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities. Cauchy's Equation and Jensen's Inequality, Prace Nauk. Uniw. Śląskiego 489, PWN & Uniw. Śląski, Warszawa-Kraków-Katowice, 1985.
  • [12] M. Kuczma, B. Choczewski and R. Ger, Iterative Functional Equations, Encyclopedia Math. Appl. 32, Cambridge Univ. Press, Cambridge, 1990.
  • [13] W. Kulpa, On the existence of maps having graphs connected and dense, Fund. Math. 76 (1972), 207-211.
  • [14] K. Kuratowski and A. Mostowski, Set Theory, Stud. Logic Found. Math. 86, PWN and North-Holland, Warszawa-Amsterdam, 1976.
  • [15] K. R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967.
  • [16] Gy. Targonski, Topics in Iteration Theory, Vandenhoeck & Ruprecht, Göttingen, 1981.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv82i2p223bwm
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