Continuous nowhere differentiable functions and related functional equations

• Autorzy: Bogdan Choczewski

Abstrakty

EN

 The aim of this survey talk is to show that recently functional equations in a single variable, also called iterative functional equations, turned out to be useful as an elementary and handful tool to study peculiar functions, in particular, continuous nowhere differentiable (cnd) functions.

Kategorie tematyczne

• 26A27: Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
• 39B42: Matrix and operator equations

Twórcy

autor

Bogdan Choczewski

• Institute of Mathematics, University of Mining and Metallurgy, al. Mickiewicza 30, 30-059 Kraków, Poland

• Książka: Different aspects of differentiability

Bibliografia

[1] P. du Bois-Reymond, Versuch einer Klassifikation der willkürlichen Funktionen reeller Argumente nach ihren Anderungen in den kleinsten Intervallen, J. Reine Angew. Math. 79 (1885), 21-37.
[2] W. F. Darsow, M. J. Frank and H.-H. Kairies, Functional equations for a function of van der Waerden type, Rad. Mat. 4 (1988), 361-374; Errata, ibid. 5 (1989), 179-180.
[3] R. Girgensohn, Funktionalgleichungen für nirgendsdifferenzierbare Funktionen, Dissertation, Mathematisch-Naturwissenschaftlichen Fakultät der Technischen Universität Clausthal, 1992, 68 pp.
[4] G. H. Hardy, Weierstrass's non-differentiable function, Trans. Amer. Math. Soc. 17 (1916), 301-325.
[5] M. Hata, Singularities of the Weierstrass type functions, J. Analyse Math. 51 (1988), 62-90.
[6] M. Kuczma, A generic property of a linear functional equation, Opuscula Math. 4 (1988), 139-144.
[7] M. Kuczma, B. Choczewski and R. Ger, Iterative Functional Equations, Encyclopedia Math. Appl. 32, Cambridge University Press, 1990.
[8] J. T. Marti, Introduction to the Theory of Bases, Springer, Berlin, 1969.
[9] E. H. Moore, On certain crinkly curves, Trans. Amer. Math. Soc. 1 (1900), 72-90.
[10] G. Peano, Sur une courbe qui remplit toute une aire plane, Math. Ann. 36 (1890), 157-160.
[11] W. Sierpiński, Sur une nouvelle courbe continue qui remplit toute une aire plane, Bull. Internat. Acad. Sci. Cracovie Cl. Sci. Math. Nat. Sér. A 1912, 462-478.

• Kolekcja: DML-PL