On the General and Measurable Solutions of some Functional Equations

Nath, Prem; Singh, Dhiraj Kumar

doi:10.1515/amsil-2017-0007

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On the General and Measurable Solutions of some Functional Equations

Annales Mathematicae Silesianae

Volume 32 (2018): Issue 1 (September 2018)

By: Prem Nath and Dhiraj Kumar Singh

Open Access

|Aug 2018

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.

References

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DOI: https://doi.org/10.1515/amsil-2017-0007 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 285 - 294

Submitted on: Sep 15, 2016

Accepted on: May 16, 2017

Published on: Aug 24, 2018

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

logarithmic function,

multiplicative function,

function measurable in the Lebesgue sense,

continuous function,

stability of a functional equation,

the Shannon entropy

Related subjects:

Mathematics,

General mathematics

© 2018 Prem Nath, Dhiraj Kumar Singh, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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