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

Hiroyoshi Oda; Makoto Tsukada; Takeshi Miura; Yuji Kobayashi; Sin-Ei Takahasi

doi:10.1155/2013/109754

International Journal of Mathematics and Mathematical Sciences (Jan 2013)

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

Hiroyoshi Oda,
Makoto Tsukada,
Takeshi Miura,
Yuji Kobayashi,
Sin-Ei Takahasi

Affiliations

Hiroyoshi Oda: Department of Information Sciences, Toho University, Funabashi, Chiba 274-8501, Japan
Makoto Tsukada: Department of Information Sciences, Toho University, Funabashi, Chiba 274-8501, Japan
Takeshi Miura: Yamagata University, Yonezawa, Yamagata 273-0866, Japan
Yuji Kobayashi: Toho University, Funabashi, Chiba 274-8501, Japan
Sin-Ei Takahasi: Toho University, Yamagata University, Funabashi, Chiba 273-0866, Japan

DOI: https://doi.org/10.1155/2013/109754
Journal volume & issue: Vol. 2013

Abstract

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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.

Published in International Journal of Mathematics and Mathematical Sciences

ISSN: 0161-1712 (Print); 1687-0425 (Online)
Publisher: Hindawi Limited
Country of publisher: United Kingdom
LCC subjects: Science: Mathematics
Website: https://www.hindawi.com/journals/ijmms/

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