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1993 | 58 | 2 | 147-159
Tytuł artykułu

On some generalized invariant means and their application to the stability of the Hyers-Ulam type

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present some extension of the concept of an invariant mean to a space of vector-valued mappings defined on a semigroup. Next, we apply it to the study of the stability of some functional equation.
Rocznik
Tom
58
Numer
2
Strony
147-159
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-06-17
poprawiono
1993-01-27
Twórcy
autor
  • Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Bibliografia
  • [1] M. A. Albert and J. A. Baker, Functions with bounded n-th differences, Ann. Polon. Math. 43 (1983), 93-103.
  • [2] K. Baron, Functions with differences in subspaces, in: Proceedings of the 18th International Symposium on Functional Equations, University of Waterloo, Faculty of Mathematics, Waterloo, Ontario, Canada, 1980.
  • [3] M. M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509-544.
  • [4] M. M. Day, Fixed point theorem for compact convex sets, ibid. 5 (1961), 585-590.
  • [5] M. M. Day, Normed Linear Spaces, Springer, Berlin 1973.
  • [6] J. Dixmier, Les moyennes invariantes dans les semigroupes et leurs applications, Acta Sci. Math. (Szeged) 12 (1950), 213-227.
  • [7] G. L. Forti and J. Schwaiger, Stability of homomorphisms and completeness, C. R. Math. Rep. Acad. Sci. Canada 11 (6) (1989), 215-220.
  • [8] Z. Gajda, A solution to a problem of J. Schwaiger, Aequationes Math. 32 (1987), 38-44.
  • [9] Z. Gajda, Invariant means and representations of semigroups in the theory of functional equations, Prace Naukowe Uniwersytetu Śląskiego 1273, Katowice 1992.
  • [10] Z. Gajda, W. Smajdor and A. Smajdor, A theorem of the Hahn-Banach type and its applications, Ann. Polon. Math. 57 (1992), 243-252.
  • [11] F. P. Greenleaf, Invariant Means on Topological Groups and Their Applications, Van Nostrand Math. Stud. 16, New York 1969.
  • [12] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I, Springer, Berlin 1963.
  • [13] D. H. Hyers, On the stability of the linear functional equations, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224.
  • [14] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Polish Scientific Publishers (PWN) and Silesian University Press, Warszawa-Kraków-Katowice 1985.
  • [15] Z. Moszner, Sur la stabilité de l'équation d'homomorphisme, Aequationes Math. 29 (1985), 290-306.
  • [16] L. Nachbin, A theorem of the Hahn-Banach type for linear transformations, Trans. Amer. Math. Soc. 68 (1950), 28-46.
  • [17] J. von Neumann, Zur allgemeinen Theorie der Masses, Fund. Math. 13 (1929), 73-116.
  • [18] K. Nikodem, On Jensen's functional equation for set-valued functions, Rad. Mat. 3 (1987), 23-33.
  • [19] J. Rätz, On approximately additive mappings, in: General Inequalities 2, Internat. Ser. Numer. Math. 47, Birkhäuser, Basel 1980, 233-251.
  • [20] L. Székelyhidi, Remark 17, Report of Meeting, Aequationes Math. 29 (1985), 95-96.
  • [21] L. Székelyhidi, Note on Hyers's theorem, C. R. Math. Rep. Acad. Sci. Canada 8 (1986), 127-129.
  • [22] S. M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York 1960.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv58z2p147bwm
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