A fixed point approach to stability of a quadratic equation
By Madjid Mirzavaziri, Mohammad Sal Moslehian. 2005
225 citations recorded by the source corpus.
Abstract.Using the fixed point alternative theorem we establish the orthogonal stability of the quadratic functional equation of Pexider type f (x+y)+g(x−y) = h(x)+k(y), where f, g, h, k are mappings from a symmetric orthogonality space to a Banach space, by orthogonal additive mappings under a necessary and sufficient condition on f.
Subfields: Applied Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/857b66deb3e5db1f7c808750248366fb2d7fd7b3
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In Applied Mathematics
- Jianlian Cui
- Choonkill Park
- Rassias Th.M.
- Janusz Brzdek
- Hamid Khodaei
- Krzysztof Cieplinski
- Mohammad Sal Moslehian
In Numerical Analysis
Citations in the corpus
- Hyperstability of the Cauchy equation on restricted domains (2013, methodology): “The fixed point results have been already used for proving stability of functional equation for instance in [2,9,28–30,34,35] and our method can be considered to be an extension of those investigations (for a survey on this subject see [10]).”
- Generalized stability of C* -ternary quadratic mappings (2007, background): “(1.4) Recently, a fixed point approach to the stability of Pexiderized quadratic equation was established by Mirzavaziri and Moslehian [14].”
- STABILITY OF MAPPINGS ON MULTI-NORMED SPACES (2007, unknown): “Moreover, we prove a generalized Hyers–Ulam–Rassias stability theorem associated to the Cauchy additive equation for mappings from linear spaces into multi-normed spaces by using a fixed point approach in the style of [4, 11, 17].”
- Approximately generalized additive functions in several variables (2010, methodology): “Using such a clever idea, they could present a short, simple proof for the Hyers-Ulam stability of Cauchy and Jensen functional equations (see also [18, 40, 53]).”