On generalizations of the Pompeiu functional equation

Pl. Kannappan and P. K. Sahoo

International Journal of Mathematics and Mathematical Sciences, 1998, vol. 21, 1-8

Abstract:

In this paper, we determine the general solution of the functional equations f ( x + y + x y ) = p ( x ) + q ( y ) + g ( x ) h ( y ) , ( ∀ x , y ∈ ℜ * ) and f ( a x + b y + c x y ) = f ( x ) + f ( y ) + f ( x ) f ( y ) , ( ∀ x , y ∈ ℜ ) which are generalizations of a functional equation studied by Pompeiu. We present a method which is simple and direct to determine the general solutions of the above equations without any regularity assumptions.

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:982654

DOI: 10.1155/S0161171298000155

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