On the general and measurable solutions of some functional equations



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.


Keywords

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

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Published : 2017-08-05


NathP., & SinghD. K. (2017). On the general and measurable solutions of some functional equations. Annales Mathematicae Silesianae, 32, 285-294. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/13927

Prem Nath 
Department of Mathematics, University of Delhi, India  India
Dhiraj Kumar Singh  dhiraj426@rediffmail.com
Department of Mathematics, Zakir Husain Delhi College (University of Delhi), India  India



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