Have a personal or library account? Click to login

Cauchy functional equation and generalized continuity

Tatra Mountains Mathematical Publications
Volume 44 (2009): Issue 1 (December 2009)
By:
Open Access
|Nov 2012

References

  1. [1] BORS´IK, J.-DOBOˇS, J.: On simple continuity points, Real Anal. Exchange 16 (1991), 552-558.10.2307/44153736
    Search in Google Scholar
  2. [2] DOBOˇS, J.: Simple continuity and cliquishnees, ˇCas. Pˇest. Mat. 112 (1987), 355-358.
    Search in Google Scholar
  3. [3] GENTRY, K. R.-HOYLE, H. B.: Somewhat continuous functions, Czechoslovak. Math. J. 21 (1971), 5-12.10.21136/CMJ.1971.100999
    Search in Google Scholar
  4. [4] GRANDE, Z.: Sur les fonctions A-continues, Demonstratio Math. 11 (1978), 519-526.
    Search in Google Scholar
  5. [5] JONES, F. B.: Connected and disconnected plane sets and the functional equation f(x + y) = f(x) + f(y), Bull. Amer. Math. Soc. 48 (1942), 115-120.10.1090/S0002-9904-1942-07615-4
    Search in Google Scholar
  6. [6] KELLUM, K. R.: Sums and limits of almost continuous functions, Colloq. Math. 31 (1974), 125-128.10.4064/cm-31-1-125-128
    Search in Google Scholar
  7. [7] KESTELMAN, H.: On the equation f(x + y) = f(x) + f(y), Fund. Math. 34 (1947), 144-147.10.4064/fm-34-1-144-147
    Search in Google Scholar
  8. [8] KOSTYRKO, P.-ˇSAL´AT, T.: On functions with closed graphs, ˇCas. Pˇest. Mat. 89 (1984), 426-432. (In Russian)
    Search in Google Scholar
  9. [9] KUCZMA, K.: An Introduction to the Theory of Functional Equations and Inequalities, PWN, Warszawa, 1965.
    Search in Google Scholar
  10. [10] LUKEˇS, J. A KOL.: Probl´emy z Matematick´e Anal´yzy, SPN, Praha, 1972. (In Czech)
    Search in Google Scholar
  11. [11] MARCUS, S.: Sur le fonctions quasicontinues au sens de S. Kempisty, Colloq. Math. 8 (1961), 47-53.10.4064/cm-8-1-47-53
    Search in Google Scholar
  12. [12] NEUBRUNNOV´A, A.-ˇSAL´AT, T.: On almost quasicontinuity, Math. Bohem. 117 (1992), 197-205.10.21136/MB.1992.125901
    Search in Google Scholar
  13. [13] NOIRI, T.: On weakly continuous mappings, Proc. Amer.Math. Soc. 46 (1974), 120-124.10.1090/S0002-9939-1974-0348698-5
    Search in Google Scholar
  14. [14] PREISS, D.: A note on symmetrically continous mappings, ˇCas. Pˇest. Mat. 96 (1971), 262-264.
    Search in Google Scholar
  15. [15] ROSEN, H.: On characterizing extentable conectivity functions by associated sets, Real Anal. Exchange 22 (1996-97), 279-283.10.2307/44152750
    Search in Google Scholar
  16. [16] SINGAL, M. K.-SINGAL, A. R.: Almost continuous mappings, Yokohama Math. J. 16 (1968), 63-73.
    Search in Google Scholar
  17. [17] SM´ITAL, J.-ˇSAL´AT, T.: Remarks on two generalizations of the notion of continuity, Acta Fac. Rer. Nat. Univ. Com. 36 (1980), 115-116.
    Search in Google Scholar
  18. [18] STALLINGS, J.: Fixed point theorem for connectivity maps, Fund. Math. 47 (1959), 249-263.10.4064/fm-47-3-249-263
    Search in Google Scholar
  19. [19] ˇSAL´AT, T.: Some generalizations of the notion of continuity and Denjoy property of functions, ˇCas. Pˇest. Mat. 99 (1974), 380-385.
    Search in Google Scholar
  20. [20] THOMSON, B. S.: Symmetric Properties of Real Functions, Marcel Dekker, New York, 1994.
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10127-009-0043-4 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Journal RSS Feed
Language: English
Page range: 9 - 14
Published on: Nov 12, 2012
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 times per year
Keywords:
Cauchy functional equation,
generalized continuity
Related subjects:
Mathematics,
General mathematics

© 2012 Pavel Kostyrko, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Previous articleVolume 44 (2009): Issue 1 (December 2009)Next article