Stability of Exponential Functional Equations with Involutions

Abstract EN

Let S be a commutative semigroup if not otherwise specified and f:S→ℝ.

In this paper we consider the stability of exponential functional equations |f(x+σ(y))-g(x)f(y)|≤ϕ(x) or ϕ(y), |f(x+σ(y))-f(x)g(y)|≤ϕ(x) or ϕ(y) for all x,y∈S and where σ:S→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); Chávez and Sahoo (2011); Houston and Sahoo (2008); Jung and Bae (2003)) and a generalized result of Albert and Baker (1982).