Stability of the multi-Jensen equation
Stability of the multi-Jensen equation
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DOI：
10.1016/j.jmaa.2009.08.021
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发表时间：
2010-03
影响因子：
1.3
通讯作者：
K. Ciepliński
中科院分区：
文献类型：
--
作者：
K. Ciepliński
In 2005 W. Prager and J. Schwaiger (see [13]) introduced the notion of multi-Jensen functions (we say that they satisfy multi-Jensen equation) f: V n−→ W (V and W being vector spaces over the rationals) with the connection with generalized polynomials and obtained their general form. The aim of this note is to investigate the stability of the multi-Jensen equation.Speaking of the stability of a functional equation we follow the question of S. Ulam:“when is it true that the solution of an equation differing slightly from a given one, must of necessity be close to the solution of the given equation?”(see [17]). As the words “differing slightly” and “be close” may have various meanings, different kinds of stability can be dealt with (see for instance [2, 7, 12, 15]).
