Stability of Exponential Functional Equations with Involutions

作者：Chung Jaeyoung; Chung Soon Yeong^*

来源：Journal of Function Spaces, 2014, 2014: 619710.

DOI：10.1155/2014/619710

Let S be a commutative semigroup if not otherwise specified and f : S -%26gt; R. In this paper we consider the stability of exponential functional equations vertical bar f(x + sigma(y)) - g(x)f(y)vertical bar %26lt;= phi(x) or phi(y), vertical bar f(x + sigma(y)) - f(x)g(y)vertical bar %26lt;= phi(x) or phi(y) for all x, y is an element of S and where sigma : S -%26gt; S is an involution. As main results we investigate bounded and unbounded functions satisfying the above inequalities. As consequences of our results we obtain the Ulam-Hyers stability of functional equations (Chung and Chang (in press); Chavez and Sahoo (2011); Houston and Sahoo (2008); Jung and Bae (2003)) and a generalized result of Albert and Baker (1982).

• 出版日期2014