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Stability of a quadratic functional equation in quasi--Banach spaces

Fridoun Moradlou|Abbas Najati
대한수학회 (The Korean Mathematical Society)|2008.09|대한수학회보 (Bulletin of the KMS)|제45권 제3호|pp. 587-600

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quadratic functionHyers–Ulam–Rassias stabilityquasi-Banach spacep-Banach space
주제분류수학

초록

In this paper we establish the general solution and investigate the Hyers–Ulam–Rassias stability of the following functional equation in quasi-Banach spaces. [수식] where Iij = {1, 2, 3, 4}＼{i, j} for all 1 ≤ i < j ≤ 4. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.

Abstract

In this paper we establish the general solution and investigate the Hyers–Ulam–Rassias stability of the following functional equation in quasi-Banach spaces. [수식] where Iij = {1, 2, 3, 4}＼{i, j} for all 1 ≤ i < j ≤ 4. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.

참고문헌 (16)

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  5. S. Czerwik, "On the stability of the quadratic mapping in normed spaces", Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 62, pp.59~64 (1992)
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  8. D. H. Hyers, "On the stability of the linear functional equation", The Proceedings of the National Academy of Sciences, 27, pp.222~224 (1941)
  9. P. Jordan, "On inner products in linear, metric spaces", Annals of Mathematics (2), 36(3), pp.718~723 (1935)
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  12. A. Najati, "Stability of a functional equation deriving from quadratic and additive functions in quasi-Banach spa", Journal of Mathematical Analysis and Applications, 337(1), pp.399~415 (2008)
  13. Th. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proceedings of the American Mathematical Society, 72(2), pp.297~300 (1978)
  14. S. Rolewicz, "Metric Linear Spaces, PWN—.Polish Scientific Publishers" (1984), D. Reidel Publishing Co.
  15. F. Skof, "Local properties and approximation of operators", Rendiconti del Seminario Matematico e Fisico di Milano, 53, pp.113~129 (1983)
  16. S. M. Ulam, "A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no 8" (1960), Interscience Publishers

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