<abstract xmlns="http://www.w3.org/1999/xhtml"><p> The general solutions of two functional equations, without imposing any regularity condition on any of the functions appearing, have been obtained. From these general solutions, the Lebesgue measurable solutions have been deduced by assuming the function(s) to be measurable in the Lebesgue sense.</p></abstract>

The general solutions of two functional equations, without imposing any regularity condition on any of the functions appearing, have been obtained. From these general solutions, the Lebesgue measurable solutions have been deduced by assuming the function(s) to be measurable in the Lebesgue sense.

On the General and Measurable Solutions of some Functional Equations

Annales Mathematicae Silesianae

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

{"article-title":"On the General and Measurable Solutions of some Functional Equations"}

The general solutions of two functional equations, without imposing any regularity condition on any of the functions appearing, have been obtained. From these...

On the General and Measurable Solutions of some Functional Equations

Published Online: Aug 24, 2018

Page range: 285 - 294

Received: Sep 15, 2016

Accepted: May 16, 2017

DOI: https://doi.org/10.1515/amsil-2017-0007

Keywords
logarithmic function, multiplicative function, function measurable in the Lebesgue sense, continuous function, stability of a functional equation, the Shannon entropy

© 2018 Prem Nath, published by Sciendo

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

On the General and Measurable Solutions of some Functional Equations

Published Online: Aug 24, 2018

Page range: 285 - 294

Received: Sep 15, 2016

Accepted: May 16, 2017

DOI: https://doi.org/10.1515/amsil-2017-0007

Keywordslogarithmic function, multiplicative function, function measurable in the Lebesgue sense, continuous function, stability of a functional equation, the Shannon entropy

© 2018 Prem Nath, published by Sciendo

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

Keywords
logarithmic function, multiplicative function, function measurable in the Lebesgue sense, continuous function, stability of a functional equation, the Shannon entropy