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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Department of Mathematics, University of Delhi, India India
Department of Mathematics, Zakir Husain Delhi College (University of Delhi), India India
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