Displaying similar documents to “Practical Ulam-Hyers-Rassias stability for nonlinear equations”

A note on the Hyers-Ulam problem

Yunbai Dong (2015)

Colloquium Mathematicae

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Let X,Y be real Banach spaces and ε > 0. Suppose that f:X → Y is a surjective map satisfying | ∥f(x)-f(y)∥ - ∥x-y∥ | ≤ ε for all x,y ∈ X. Hyers and Ulam asked whether there exists an isometry U and a constant K such that ∥f(x) - Ux∥ ≤ Kε for all x ∈ X. It is well-known that the answer to the Hyers-Ulam problem is positive and K = 2 is the best possible solution with assumption f(0) = U0 = 0. In this paper, using the idea of Figiel's theorem on nonsurjective isometries, we give a new...

Stability analysis of implicit fractional differential equations with anti-periodic integral boundary value problem

Akbar Zada, Hira Waheed (2020)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability, and generalized Ulam-Hyers-Rassias stability of the solution to an implicit nonlinear fractional differential equations corresponding to an implicit integral boundary condition. We develop conditions for the existence and uniqueness by using the classical fixed point theorems such as Banach contraction...