<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

Publié en ligne: 24 août 2018

Pages: 215 - 225

Reçu: 30 sept. 2017

Accepté: 11 avr. 2018

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

Mots clés
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

Publié en ligne: 24 août 2018

Pages: 215 - 225

Reçu: 30 sept. 2017

Accepté: 11 avr. 2018

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

Mots clésstability 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.

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