On the Ulam stability of F(z) + F(2z) = 0
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Title: | On the Ulam stability of F(z) + F(2z) = 0 |
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Authors: | Mora, Gaspar |
Research Group/s: | Curvas Alpha-Densas. Análisis y Geometría Local |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Spaces of bounded analytic functions of one complex variable | Approximation | Functional equations in the complex plane |
Knowledge Area: | Análisis Matemático |
Issue Date: | 8-Apr-2020 |
Publisher: | Springer Nature |
Citation: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 2020, 114:108. doi:10.1007/s13398-020-00846-y |
Abstract: | In this paper it is shown that the complex functional equation F(z) + F(2z) = 0, z ∈ Ω := C\(−∞, 0], is stable in the strong sense of Ulam. It means that given an analytic and bounded function f (z) on Ω satisfying | f (z) + f (2z)| < δ, z ∈ Ω, for some δ > 0, there exists an analytic solution F(z) of the above functional equation such that | f (z) − F(z)| < K(δ) on each compact A of Ω, where K(δ) is a positive real function that tends to 0 as δ → 0. This result is extended to analytic functions f (z) on Ω satisfying | f (z)+ f (2z)| < δ, z ∈ Ω, for some δ > 0, not necessarily bounded on Ω. |
URI: | http://hdl.handle.net/10045/105470 |
ISSN: | 1578-7303 (Print) | 1579-1505 (Online) |
DOI: | 10.1007/s13398-020-00846-y |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © The Royal Academy of Sciences, Madrid 2020 |
Peer Review: | si |
Publisher version: | https://doi.org/10.1007/s13398-020-00846-y |
Appears in Collections: | INV - CADAGL - Artículos de Revistas |
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Mora_2020_RACSAM_final.pdf | Versión final (acceso restringido) | 234,1 kB | Adobe PDF | Open Request a copy |
Mora_2020_RACSAM_preprint.pdf | Preprint (acceso abierto) | 121,83 kB | Adobe PDF | Open Preview |
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