Hyers-Ulam stability of nonlinear integral equation.

Gachpazan, Mortaza; Baghani, Omid

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Hyers-Ulam stability of the delay equation $y^{'} (t) = λ y (t - τ)$ .

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A fixed point approach to the stability of the functional equation $f (x + y) = F [f (x), f (y)]$ .

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Practical Ulam-Hyers-Rassias stability for nonlinear equations

Jin Rong Wang, Michal Fečkan (2017)

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In this paper, we offer a new stability concept, practical Ulam-Hyers-Rassias stability, for nonlinear equations in Banach spaces, which consists in a restriction of Ulam-Hyers-Rassias stability to bounded subsets. We derive some interesting sufficient conditions on practical Ulam-Hyers-Rassias stability from a nonlinear functional analysis point of view. Our method is based on solving nonlinear equations via homotopy method together with Bihari inequality result. Then we consider nonlinear...