Advertisement

aequationes mathematicae

, Volume 28, Issue 1, pp 22–34 | Cite as

On approximate solutions of functional equations of countable order

  • Karol Baron
  • Witold Jarczyk
Research Paper

AMS (1980) subject classification

Primary 39B10 Secondary 39B70 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Baron, K.,On approximate solutions of a functional equation. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys.23 (1975), 1065–1068.Google Scholar
  2. [2]
    Baron, K.,On extending solutions of a functional equation. Aequationes Math.13 (1975), 285–288.Google Scholar
  3. [3]
    Baron, K.,Functional equations of infinite order. Prace Nauk. Uniw. Sl⇂sk. w Katowicach (Scientific Publications of the University of Silesia)265, Uniw. Śl⇂ski, Katowice, 1978.Google Scholar
  4. [4]
    Baron, K.,On a majorization of distances between the values of a family of functions and a fixed point. In:General inequalities 2, 2nd International Conference on General Inequalities (International Series of Numerical Mathematics 27) Birkhäuser, Basel, 1980, pp. 463–464.Google Scholar
  5. [5]
    Baron, K.,On approximate solutions of a system of functional equations. To appear in Ann. Polon. Math.Google Scholar
  6. [6]
    Bessaga, Cz.,On the converse of the Banach “fixed-point principle”. Colloq. Math.7 (1959), 41–43.Google Scholar
  7. [7]
    Bessaga, Cz. andPelczyński, A.,Selected topics in infinite-dimensional topology. Monografie Mat. Vol. 58, Polish Scientific Publishers, Warszawa, 1975.Google Scholar
  8. [8]
    Buck, R. C.,On approximation theory and functional equations. J. Approximation Theory5 (1972), 228–237.Google Scholar
  9. [9]
    Buck, R. C.,Approximation theory and functional equations II. J. Approximation Theory9 (1973), 121–125.Google Scholar
  10. [10]
    Dugundji, J.,An extension of Tietze's theorem. Pacific J. Math.1 (1951), 353–367.Google Scholar
  11. [11]
    Dugundji, J. andGranas, A.,Fixed point theory I. Monografie Mat. Vol. 61, Polish Scientific Publishers, Warszawa, 1982.Google Scholar
  12. [12]
    Edelstein, M.,A short proof of a theorem of L. Janos. Proc. Amer. Math. Soc.20 (1969), 509–510.Google Scholar
  13. [13]
    Hyers, D. H.,On the stability of the linear functional equation. Proc. Nat. Acad. Sci. U.S.A.27 (1941), 222–224.Google Scholar
  14. [14]
    Jarczyk, W.,Generic properties of nonlinear functional equations. To appear in Aequationes Math.26 (1983), 40–53.Google Scholar
  15. [15]
    Kuczma, M.,Functional equations in a single variable. Monografie Mat. Vol. 46, Polish Scientific Publishers, Warszawa, 1968.Google Scholar
  16. [16]
    Leader, S.,Uniformly contractive fixed points in compact metric spaces. Proc. Amer. Math. Soc.86 (1982), 153–158.Google Scholar
  17. [17]
    Myers, P. R.,A converse to Banach's contraction theorem. J. Res. Nat. Bur. Standards B71 (1967), 73–76.Google Scholar
  18. [18]
    Opoicev, V. I.,A converse of the contraction mapping principle (Russian). Uspehi Mat. Nauk31 (1976), no. 4, 169–198.Google Scholar
  19. [19]
    Pólya, G. andSzegö, G.,Problems and theorems in analysis, vol. I. Springer, Berlin-Heidelberg-New York, 1972–1976.Google Scholar

Copyright information

© Birkhäuser Verlag 1985

Authors and Affiliations

  • Karol Baron
    • 1
  • Witold Jarczyk
    • 1
  1. 1.Department of MathematicsSilesian UniversityKatowicePoland

Personalised recommendations