충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제36권4호
  • /
  • Pages.267-277
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  • 2023
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
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ON ADDITIVE MAPPINGS WITH BOUNDED VALUE NEAR A POINT

  • Won-Gil Park (Department of Mathematics Education, Mokwon University) ;
  • Ick-Soon Chang (Department of Mathematics, Chungnam National University) ;
  • Jaiok Roh (Ilsong Liberal Art Schools (Mathematics), Hallym University)
  • 투고 : 2023.10.21
  • 심사 : 2023.11.16
  • 발행 : 2023.11.30
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초록

In this paper, we will first prove the linearity of additive mappings with bounded value near a point. And by using our theorem we will investigate the instability of the Cauchy equation in ℝ2.

키워드

과제정보

This work was supported by National Research Foundation of Korea(NRF) grant funded by the Korea government (MSIT) (No. 2021R1A2C109489611).

참고문헌

  1. A. L. Cauchy, Cours d'Analyse de l'Ecole Polytechnique, 1, Analyse algebrique, V. Paris, 1821.
  2. Z. Gajda, On stability of additive mappings, Internat. J. Math. & Math. Sci., 14 (1991), 431-434. https://doi.org/10.1155/S016117129100056X
  3. H. Kestelman, On the functional equation f(x + y) = f(x) + f(y), Fund. Math., 34 (1946), 144-147. https://doi.org/10.4064/fm-34-1-144-147
  4. D. Reem, The Cauchy functional equation as an initial value problem, homomorphisms and tori, arXiv:1002.3721v2 [math.CA] (2010), 1-6