Results in Mathematics

, Volume 35, Issue 1–2, pp 23–31 | Cite as

Bounded Solutions of n-Cocycle And Related Equations on Amenable Semigroups



The cocycle functional equation, originating in group theory and playing a role in such areas as cohomology, polyhedral algebra, and information theory, has a long and rich history. Cocycles of higher orders have been introduced in cohomology theory. This paper presents the bounded solutions of cocycle equations of all orders on amenable semigroups. Some related functional equations are treated also. These results generalize some recent results of Pales and Szekelyhidi.


amenable semigroup invariant mean functional equations for functions of several variables cocycle coboundary n-cocycle n-coboundary Pexider equations 

1991 Mathematics Subject Classification



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Badora, On approximately additive functions, Annales Math. Silesianae 8 (1994), 111–126.MathSciNetGoogle Scholar
  2. 2.
    T. M. K. Davison and B. R. Ebanks, Cocycles on cancellative semigroups, Publ. Math. Debrecen 46(1995), 137–147.MathSciNetMATHGoogle Scholar
  3. 3.
    B. R. Ebanks, Branching measures of information on strings, Canad. Math. Bull. 22 (1979), 433–448.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    S. Eilenberg and S. Maclane, Determination of the second homology and cohomology groups of a space by means of homotopy invariants, Proc. Nat. Acad. Sci. U. S. A. 32(11) (1946), 277–289.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    J. Erdos, A remark on the paper “On some functional equations” by S. Kurepa, Glasnik Mat.-Fiz. Astronom. (2) 14 (1959), 3-5.Google Scholar
  6. 6.
    Z. Gajda, Generalized invariant means and their application to the stability of homomorphisms (preprint).Google Scholar
  7. 7.
    P. Greeenleaf, Invariant means on topological groups, Van Nostrand, 1969.Google Scholar
  8. 8.
    E. Hewitt and K. Ross, Abstract Harmonic Analysis, Springer, 1963.Google Scholar
  9. 9.
    B. Jessen, J. Karpf, and A. Thorup, Some functional equations in groups and rings, Math. Scand. 22 (1968), 257–265.MathSciNetMATHGoogle Scholar
  10. 10.
    S. Kurepa, On some functional equations, Glasnik Mat.-Fiz. Astronom. (2) 11 (1956), 3-5.Google Scholar
  11. 11.
    Z. Pales, Bounded solutions and stability of functional equations for two variable functions, Results in Math. 26 (1994), 360–265.MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    L. Szekelyhidi, Stability properies of functional equations in several variables, Publ. Math. Debrecen 47 (1995), 95–100.MathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  1. 1.Department of MathematicsMarshall UniversityHuntingtonUSA

Personalised recommendations