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Hyers-Ulam-Rassias Stability of the Banach Space Valued Linear Differential Equations y' = λy

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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differential equationHyers-Ulam-Rassias stability
주제분류수학

초록

The aim of this paper is to prove the stability in the sense ofHyers-Ulam-Rassias of the Banach space valued differentialequation y' = lambda y, where lambda is a complex constant.That is, suppose f is a Banach space valued stronglydifferentiable function on an open interval. If f is anapproximate solution of the equation y' = lambda y, then thereexists an exact solution of the equation near to f.

Abstract

The aim of this paper is to prove the stability in the sense ofHyers-Ulam-Rassias of the Banach space valued differentialequation y' = lambda y, where lambda is a complex constant.That is, suppose f is a Banach space valued stronglydifferentiable function on an open interval. If f is anapproximate solution of the equation y' = lambda y, then thereexists an exact solution of the equation near to f.

참고문헌 (11)

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  2. "On stability of additive mappings", 1991, pp.14, 431~
  3. "On the stability of the linear functionalequation", 1941, pp.27, 222~
  4. "Hyers-Ulam-Rassias stability of linear differentialequations", ~
  5. "Hyers-Ulam stability of linear differential operatorwith constant coefficients", 258, pp.90~96 (2003)
  6. "A characterization of Hyers-Ulam stability of firstorder linear differential operators", 286, pp.136~146 (2003)
  7. "On the stability of the linear mapping in Banach spaces", 1978, pp.72, 297~
  8. "On the behavior of mappings which do not satisfyHyers-Ulam stability", 1992, 989~
  9. "Real and Complex Analysis", (3rd Edition, 1987., ~[DOI]
  10. "On the Hyers-Ulam stability of the Banach space-valueddifferential equation y' = lambda y", 39, pp.309~315 (2002)
  11. "Problems in Modern Mathematics", 1964., pp.vi, ~

관련 논문AI추천

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 Miura대한수학회 · 대한수학회지2004 · 제41권 제6호On the Hyers-Ulam stability of the Banach space-valued differential equation y' = lambda yShizuo Miyajima, Sin-Ei Takahasi, Takeshi Miura대한수학회 · 대한수학회보2002 · 제39권 제2호ON HYERS-ULAM STABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS정순모, Jinghao Huang, Yongjin Li대한수학회 · 대한수학회보2015 · 제52권 제2호HYERS-ULAM STABILITY OF AN ADDITIVE (ρ1, ρ2)-FUNCTIONAL INEQUALITY IN BANACH SPACES박춘길, Sungsik Yun한국수학교육학회 · 이론수학과 교직수학2018 · 제25권 제2호Hyers--Ulam and Hyers--Ulam Rassias stability of Caputo fractional linear differential equationsAlaa E. Hamza, Karima M. Oraby대한수학회 · 대한수학회논문집2025 · 제40권 제4호An additive functional inequality박춘길, 신동윤, 이성진강원경기수학회 · 한국수학논문집2014 · 제22권 제2호

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