Stability of Functional Equations in Dislocated Quasi-Metric Spaces

Abstract

We present a result on the generalized Hyers-Ulam stability of a functional equation in a single variable for functions that have values in a complete dislocated quasi-metric space. Next, we show how to apply it to prove stability of the Cauchy functional equation and the linear functional equation in two variables, also for functions taking values in a complete dislocated quasimetric space. In this way we generalize some earlier results proved for classical complete metric spaces.

Keywords

• stability of functional equations
• square symmetric groupoid
• dislocated quasi-metric space
• semigroup
• Cauchy equation