The Ulam Type Stability of a Generalized Additive Mapping and Concrete Examples

The Ulam Type Stability of a Generalized Additive Mapping and Concrete Examples

We give an Ulam type stability result for the following functional equation: f(αx−αx′+x0)=βf(x)−βf(x′)+y0  (for all  x,x′∈X) under a suitable condition. We also give a concrete stability result for the case taking up δ∥x∥p∥x′∥q as a control function.

Bibliographic Details
Main Authors: Hiroyoshi Oda, Makoto Tsukada, Takeshi Miura, Yuji Kobayashi, Sin-Ei Takahasi
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2013/109754
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spelling doaj-afde1d0790484187b943e61486a9ceac2020-11-24T22:58:10ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252013-01-01201310.1155/2013/109754109754The Ulam Type Stability of a Generalized Additive Mapping and Concrete ExamplesHiroyoshi Oda0Makoto Tsukada1Takeshi Miura2Yuji Kobayashi3Sin-Ei Takahasi4Department of Information Sciences, Toho University, Funabashi, Chiba 274-8501, JapanDepartment of Information Sciences, Toho University, Funabashi, Chiba 274-8501, JapanYamagata University, Yonezawa, Yamagata 273-0866, JapanToho University, Funabashi, Chiba 274-8501, JapanToho University, Yamagata University, Funabashi, Chiba 273-0866, JapanWe give an Ulam type stability result for the following functional equation: f(αx−αx′+x0)=βf(x)−βf(x′)+y0  (for all  x,x′∈X) under a suitable condition. We also give a concrete stability result for the case taking up δ∥x∥p∥x′∥q as a control function.http://dx.doi.org/10.1155/2013/109754
collection DOAJ
language English
format Article
sources DOAJ
author Hiroyoshi Oda
Makoto Tsukada
Takeshi Miura
Yuji Kobayashi
Sin-Ei Takahasi
spellingShingle Hiroyoshi Oda
Makoto Tsukada
Takeshi Miura
Yuji Kobayashi
Sin-Ei Takahasi
The Ulam Type Stability of a Generalized Additive Mapping and Concrete Examples
International Journal of Mathematics and Mathematical Sciences
author_facet Hiroyoshi Oda
Makoto Tsukada
Takeshi Miura
Yuji Kobayashi
Sin-Ei Takahasi
author_sort Hiroyoshi Oda
title The Ulam Type Stability of a Generalized Additive Mapping and Concrete Examples
title_short The Ulam Type Stability of a Generalized Additive Mapping and Concrete Examples
title_full The Ulam Type Stability of a Generalized Additive Mapping and Concrete Examples
title_fullStr The Ulam Type Stability of a Generalized Additive Mapping and Concrete Examples
title_full_unstemmed The Ulam Type Stability of a Generalized Additive Mapping and Concrete Examples
title_sort ulam type stability of a generalized additive mapping and concrete examples
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2013-01-01
description We give an Ulam type stability result for the following functional equation: f(αx−αx′+x0)=βf(x)−βf(x′)+y0  (for all  x,x′∈X) under a suitable condition. We also give a concrete stability result for the case taking up δ∥x∥p∥x′∥q as a control function.
url http://dx.doi.org/10.1155/2013/109754
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