On generalizations of the Pompeiu functional equation
In this paper, we determine the general solution of the functional equations f(x+y+xy)=p(x)+q(y)+g(x)h(y), (∀x,y∈ℜ*) and f(ax+by+cxy)=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 determin...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000155 |
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| Summary: | In this paper, we determine the general solution of the functional equations
f(x+y+xy)=p(x)+q(y)+g(x)h(y), (∀x,y∈ℜ*)
and
f(ax+by+cxy)=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. |
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| ISSN: | 0161-1712 1687-0425 |