<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Stability of Functional Equations in Dislocated Quasi-Metric Spaces

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Stability of Functional Equations in Dislocated Quasi-Metric Spaces"}

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...

Stability of Functional Equations in Dislocated Quasi-Metric Spaces

Published Online: Aug 24, 2018

Page range: 215 - 225

Received: Sep 30, 2017

Accepted: Apr 11, 2018

DOI: https://doi.org/10.2478/amsil-2018-0005

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

© 2018 Beata Hejmej, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Stability of Functional Equations in Dislocated Quasi-Metric Spaces

Published Online: Aug 24, 2018

Page range: 215 - 225

Received: Sep 30, 2017

Accepted: Apr 11, 2018

DOI: https://doi.org/10.2478/amsil-2018-0005

Keywordsstability of functional equations, square symmetric groupoid, dislocated quasi-metric space, semigroup, Cauchy equation

© 2018 Beata Hejmej, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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