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Abstrakty
Let (X, .) be a group endowed with a topology and F : C - X. Under some assumptions on X and F, we describe the solutions f : X - > C of the functional equation f(F(y)) . x)=f(y)f(x), that are continuous at a point or (universally, Baire, Christensen or Haar) measurable. We also show some consequences of those results.
Wydawca
Czasopismo
Rocznik
Tom
Strony
859--868
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Department of Mathematics Pedagogical University Podchorążych 2, 30-084 Kraków, Poland, jbrzdek@ap.krakow.pl
Bibliografia
- [1] J. Aczél and J. Dhombres, Functional Equations in Several Variables, Encyclopedia of Mathematics and its Applications, Vol. 31, Cambridge University Press, 1989.
- [2] N. Brillouët-Belluot, Multiplicative symmetry and related functional equations, Aequationes Math. 51 (1996), 21-47.
- [3] N. Brillouët-Belluot, On Multiplicative Symmetry, in: Advances in equations and inequalities, J. M. Rassias (ed.), Hadronic Press, 1999, 31-55.
- [4] N. Brillouët-Belluot, More about some functional equations of multiplicative symmetry, Publicationes Math. Debrecen 58 (2001), 575-585.
- [5] N. Brillouët-Belluot, Pexider generalization of a functional equation of multiplicative symmetry, Publicationes Math. Debrecen 64 (2004), 107-127.
- [6] J. Brzdęk, On almost additive functions, Bull. Austral. Math. Soc. 54 (1996), 281-290.
- [7] J. P. R. Christensen, Borel structures in groups and semigroups, Math. Scan. 28 (1971), 124-128.
- [8] J. P. R. Christensen, On sets of Haar measure zero in abelian Polish groups, Israel J. Math. 13 (1972), 255-260.
- [9] Z. Daróczy, Über die Funktionalgleichung: φ(φ(x)·y)=φ(x)φ(y), Acta Univ. Debrecen Ser. Fiz. Chem. 8 (1962), 125-132.
- [10] J. G. Dhombres, Sur les opérateurs multiplicativement liés, Mém. Soc. Math. France 27 (1971).
- [11] J. G. Dhombres, Quelques equations fonctionelles provenant de la théorie des moyennes, C.R. Acad. Sci. Paris 273 (1971), 1-3.
- [12] J. G. Dhombres, Functional equations on semi-groups arising from the theory of means, Nanta Math. 5 (3) (1972), 48-66.
- [13] J. G. Dhombres, Solution générale sur une groupe abélien de l’équation fonctionnelle: f(x∗f(y))=f(y∗f(x)), Aequationes Math. 15 (1977), 173-193.
- [14] J. G. Dhombres, Some Aspects of Functional Equations, Chulalongkorn University, Department of Mathematics, Bangkok, 1979.
- [15] M. L. Dubreil-Jacotin, Propriétés algébriques des transformations de Reynolds, C.R. Acad. Sci. Paris 236 (1953), 1950-1.
- [16] P. Fisher and Z. Slodkowski, Christensen zero sets and measurable convex functions, Proc. Amer. Math. Soc. 79 (1980), 449-453.
- [17] C. F. K. Jung, V. Boonyasombat, G. Barbançon and J. R. Jung,On the functional equation f(x+f(y))=f(x)·f(y), Aequationes Math. 14 (1976), 41-48.
- [18] Y. Matras, Sur l’équation fonctionnelle: f(x·f(y)) =f(x)·f(y), Acad. Roy. Belg. Bull. Cl. Sci. (5)55 (1969), 731-751.
- [19] A. Najdecki, On stability of a functional equation connected with the Reynolds operator, J. Inequal. Appl. vol. 2007, Article ID 79816, 3 pages, 2007. doi:10.1155/2007/79816
- [20] A. Najdecki, On Stability of Some Generalizations of the Cauchy, d’Alembert and Quadratic Functional Equations, Ph.D. Thesis, Pedagogical University in Cracow, 2006 (in Polish).
- [21] J. C. Oxtoby, Measure and Category, Graduate Texts in Mathematics, Springer Verlag, 1971.
- [22] K. Stromberg, An elementary proof of Steinhaus’s theorem, Proc. Amer. Math. Soc. 36 (1972), 308.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0023-0006