2019
DOI: 10.1007/s00025-019-1132-6
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On the Stability Problem of Differential Equations in the Sense of Ulam

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Cited by 21 publications
(15 citation statements)
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“…There exists a unique linear transformation Δ : D 1 ⟶ D 2 such that the limit ΔðσÞ = lim n⟶+∞ hð2 n σÞ/2 n exists for each σ ∈ D 1 and khðσÞ − ΔðσÞk ≤ λ for all σ ∈ D 1 , which was the first step towards more answers in this area. Many researchers have analyzed the HUS of various classes of differential systems (see, for instance, [1,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]). In 1978, Rassias [22] provided a generalized answer to the Ulam question for approximate λ-linear transformations.…”
Section: Introductionmentioning
confidence: 99%
“…There exists a unique linear transformation Δ : D 1 ⟶ D 2 such that the limit ΔðσÞ = lim n⟶+∞ hð2 n σÞ/2 n exists for each σ ∈ D 1 and khðσÞ − ΔðσÞk ≤ λ for all σ ∈ D 1 , which was the first step towards more answers in this area. Many researchers have analyzed the HUS of various classes of differential systems (see, for instance, [1,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]). In 1978, Rassias [22] provided a generalized answer to the Ulam question for approximate λ-linear transformations.…”
Section: Introductionmentioning
confidence: 99%
“…In a recent paper, Jung in [21] used the fixed point approach to prove the stability of ceratin first order differential equations. In [5] Başci et al studied the stability of some differential equations in the sense of Hyers-Ulam. In [7] the authors investigated the Hyers-Ulam stability for fractional differential equations including the new Caputo-Fabrizio fractional derivative.…”
Section: Introductionmentioning
confidence: 99%
“…[5]). Define the function d :S × S → [0, ∞] with d(f, g) := inf C ∈ [0, ∞] : |f(t) − g(t)|e −At Cφ(t), t ∈ I ,where A > 0 is a given constant and φ : I → (0, ∞) is a given continuous function.…”
mentioning
confidence: 99%
“…In 1978, Rassias [2] introduced a new definition of generalized Hyers-Ulam stability by the constant ε by a variable, and obtained the stability of Hyers-Ulam-Rassias for functional equation. There is a rich literature on this topic for standard integer-order equations (see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]). In addition, the same stability concepts are introduced to find approximate solutions to fractional differential equations, see [18,19] and the references therein.…”
Section: Introductionmentioning
confidence: 99%