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Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations ${\text\bf y}' = {\text\bf\lambda y}$

Sin-Ei Takahasi|Soon-Mo Jung|Takeshi Miura
대한수학회 (The Korean Mathematical Society)|2004.11|대한수학회지 (Journal of the KMS)|제41권 제6호|pp. 995-1005

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Abstract

The aim of this paper is to prove the stability in the sense of Hyers-Ulam-Rassias of the Banach space valued differential equation y = λy, where λ is a complex constant. That is, suppose f is a Banach space valued strongly differentiable function on an open interval. If f is an approximate solution of the equation y = λy, then there exists an exact solution of the equation near to f.

참고문헌 (11)

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  4. "Hyers-Ulam-Rassias stability of linear dierential equa-tions"
  5. "-E. Takahasi,Hyers-Ulam stability of linear dier-ential operator with constant coecients", 258, pp.90~96 (2003)
  6. "A characterization of Hyers-Ulam stability of rst order linear dierentialoperators", 286, pp.136~146 (2003)
  7. "On the stability of the linear mapping in Banach spaces", 72 (1978)
  8. "On the behavior of mappings which do not satisfyHyers-Ulam stability", 114 (1992)
  9. "Real and Complex Analysis(3rd Edition" (1987), McGraw-Hill
  10. "On the Hyers-Ulam stability of theBanach space-valued dierential equationy", 39, pp.309~315 (2002)
  11. "Problems in Modern Mathematics", vi (1964)

관련 논문AI추천

On the Hyers-Ulam stability of the Banach space-valued differential equation y' = lambda yShizuo Miyajima, Sin-Ei Takahasi, Takeshi Miura대한수학회 · 대한수학회보2002 · 제39권 제2호Hyers-Ulam-Rassias Stability of the Banach Space Valued Linear Differential Equations y' = λySin-Ei Takahasi, Soon-Mo Jung, Takeshi Miura대한수학회 · 대한수학회지2004 · 제41권 제6호A note on the Hyers-Ulam-Rassias stability of a quadratic equation강지형, 이양희, 이창주대한수학회 · 대한수학회보2004 · 제41권 제3호Hyers-Ulam-Rassias stability of a system of first order linear recurrencesMingyong Xu대한수학회 · 대한수학회보2007 · 제44권 제4호ON HYERS-ULAM STABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS정순모, Jinghao Huang, Yongjin Li대한수학회 · 대한수학회보2015 · 제52권 제2호An additive functional inequality박춘길, 신동윤, 이성진강원경기수학회 · 한국수학논문집2014 · 제22권 제2호

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