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Displaying similar documents to “Almost surjective ε-isometries of Banach spaces”

The Hyers-Ulam-Aoki Type Stability of Some Functional Equations on Banach Lattices

Nutefe Kwami Agbeko (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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In Agbeko (2012) the Hyers-Ulam-Aoki stability problem was posed in Banach lattice environments with the addition in the Cauchy functional equation replaced by supremum. In the present note we restate the problem so that it relates not only to supremum but also to infimum and their various combinations. We then propose some sufficient conditions which guarantee its solution.

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...

Practical Ulam-Hyers-Rassias stability for nonlinear equations

Jin Rong Wang, Michal Fečkan (2017)

Mathematica Bohemica

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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...

Perturbations of isometries between Banach spaces

Rafał Górak (2011)

Studia Mathematica

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We prove a very general theorem concerning the estimation of the expression ||T((a+b)/2) - (Ta+Tb)/2|| for different kinds of maps T satisfying some general perturbed isometry condition. It can be seen as a quantitative generalization of the classical Mazur-Ulam theorem. The estimates improve the existing ones for bi-Lipschitz maps. As a consequence we also obtain a very simple proof of the result of Gevirtz which answers the Hyers-Ulam problem and we prove a non-linear generalization...

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...