On the General and Measurable Solutions of some Functional Equations

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 general solutions, the Lebesgue measurable solutions have been deduced by assuming the function(s) to be measurable in the Lebesgue sense.

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Veröffentlicht in:Annales mathematicae Silesianae 2018-09, Vol.32 (1), p.285-294
Hauptverfasser: Nath, Prem, Singh, Dhiraj Kumar
Format: Artikel
Sprache:eng
Schlagworte:
continuous function
function measurable in the Lebesgue sense
logarithmic function
multiplicative function
stability of a functional equation
the Shannon entropy
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Beschreibung
Zusammenfassung: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.
ISSN:0860-2107
2391-4238
DOI:10.1515/amsil-2017-0007