On generalizations of the Pompeiu functional equation. (1998)

• Record Type: Journal Article
• Authors: Kannappan, Pl.; Sahoo, P. K.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 21:Number 1(1998)
• Page Start: 117
• Page End: 124
• Publication Date: 1998
• Subjects: Pompeiu functional equation -- multiplicative function -- logarithmic function -- exponential function; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171298000155
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : In this paper, we determine the general solution of the functional equationsf ( x + y + x y ) = p ( x ) + q ( y ) + g ( x ) h ( y ), ( ∀ x, y ∈ ℜ * ) andf ( 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.