On stability of the monomial functional equation in normed spaces over fields with valuation

摘要

A stability theorem is proved for the monomial functional equation where the functions map a normed space over a field of characteristic zero with an arbitrary valuation into a Banach space over a field of characteristic zero with a valuation. Some regularity properties of the monomial functions are also discussed. (c) 2006 Elsevier Inc. All rights reserved.