Approximate homomorphisms and derivation in multi-Banach algebras

Ravi P. Agarwal, et al. "Approximate homomorphisms and derivation in multi-Banach algebras." Commentationes Mathematicae 51.1 (2011): null. <http://eudml.org/doc/292259>.

@article{RaviP2011,
abstract = {Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in multi-Banach algebras and derivations on multi-Banach algebras for the additive functional equation \[ \sum \_\{i=1\}^m f\left(mx\_i+\sum \_\{j=1, j\ne i\}^m x\_j\right) + f\left(\sum \_\{i=1\}^m x\_i\right) = 2 f \left(\sum \_\{i=1\}^\{m\} mx\_i\right) \] for each $m\in \mathbb \{N\}$ with $m\ge 2$.},
author = {Ravi P. Agarwal, Yeol Je Cho, Choonkil Park, Reza Saadati},
journal = {Commentationes Mathematicae},
keywords = {Additive functional equation; fixed point; homomorphism in multi-Banach algebra; generalized Hyers-Ulam stability; derivation on multi-Banach algebra; multi-normed space},
language = {eng},
number = {1},
pages = {null},
title = {Approximate homomorphisms and derivation in multi-Banach algebras},
url = {http://eudml.org/doc/292259},
volume = {51},
year = {2011},
}

TY - JOUR
AU - Ravi P. Agarwal
AU - Yeol Je Cho
AU - Choonkil Park
AU - Reza Saadati
TI - Approximate homomorphisms and derivation in multi-Banach algebras
JO - Commentationes Mathematicae
PY - 2011
VL - 51
IS - 1
SP - null
AB - Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in multi-Banach algebras and derivations on multi-Banach algebras for the additive functional equation \[ \sum _{i=1}^m f\left(mx_i+\sum _{j=1, j\ne i}^m x_j\right) + f\left(\sum _{i=1}^m x_i\right) = 2 f \left(\sum _{i=1}^{m} mx_i\right) \] for each $m\in \mathbb {N}$ with $m\ge 2$.
LA - eng
KW - Additive functional equation; fixed point; homomorphism in multi-Banach algebra; generalized Hyers-Ulam stability; derivation on multi-Banach algebra; multi-normed space
UR - http://eudml.org/doc/292259
ER -