충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제35권2호
  • /
  • Pages.149-159
  • /
  • 2022
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

A NOTE ON FUNCTIONAL INEQUALITY AND ADDITIVE MAPPING

  • Chang, Ick-Soon (Department of Mathematics, Chungnam National University) ;
  • Lee, Hyun-Wook (Department of Mathematics, Chungnam National University) ;
  • Kim, Hark-Mahn (Department of Mathematics, Chungnam National University)
  • 투고 : 2022.01.20
  • 심사 : 2022.02.16
  • 발행 : 2022.05.15
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this note, we prove some theorems concerning the stability of functional inequality associated with additive mappings on quasi-𝛽-normed spaces.

키워드

참고문헌

  1. Y. Benyamini and J. Lindenstrauss, Geometric Nonlinear Functional Analysis, Vol. 1, Colloq. Publ. 48 Amer. Math. Soc., Providence, 2000.
  2. W. Fechner, Stability of a functional inequalities associated with the Jordan-von Neumann functional equation, Aequationes Math., 71 (2006), 149-161. https://doi.org/10.1007/s00010-005-2775-9
  3. Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci., 14 (1991), 431-434. https://doi.org/10.1155/S016117129100056X
  4. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211
  5. A. Gilanyi, Eine zur Parallelogrammgleichung aquivalente Ungleichung, Aequationes Math., 62 (2001), 303-309. https://doi.org/10.1007/PL00000156
  6. A. Gilanyi, On a problem by K. Nikodem, Math. Inequal. Appl., 5 (2002), 707-710.
  7. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci., U.S.A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  8. A. Najati and M. B. Moghimi, Stability of a functional equation deriving from quadratic and additive function in quasi-Banach spaces, J. Math. Anal. Appl., 337 (2008), 399-415. https://doi.org/10.1016/j.jmaa.2007.03.104
  9. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  10. J. Ratz, On inequalities associated with the Jordan-von Neumann functional equation, Aequationes Math., 66 (2003), 191-200. https://doi.org/10.1007/s00010-003-2684-8
  11. S. Rolewicz, Metric Linear Spaces, Reidel and Dordrecht, and PWN-Polish Sci., Publ. 1984.
  12. S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960.