Hyperstability and Superstability

By Janusz Brzdek, Krzysztof Cieplinski. 2013

146 citations recorded by the source corpus.

This is a survey paper concerning the notions of hyperstability and superstability, which are connected to the issue of Ulam’s type stability. We present the recent results on those subjects.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/6866b0d8617ed2742663d240f70dc9a52bb37bf0

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

On Ulam’s Type Stability of the Linear Equation and Related Issues (2014, background): “In this paper, we focus on stability of a linear functional equation of the first order, in single variable and some related results; in this way, we complement to some extent the information provided in surveys [7–9, 25, 26].”
Fixed Point Theory and the Ulam Stability (2014, background): “Rassias concerning optimality of estimations in Theorem 29) and in [69] (in proving stability of the equation ofp-Wright affine functions); in particular, it has been discovered in this way in [49] that the property of hyperstability for the additive Cauchy equation appears quite often in a natural ”
ON HYPERSTABILITY OF GENERALISED LINEAR FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES (2015, unknown): “Let f : X → Y be a mapping such that Then there exists exactly one quadratic mapping Q : The investigation of hyperstability is a new area of research; see, for example, [11].”