2009 / March Volume 4 No.1
On a functional equation associated with the trapezoidal rule-II
| Published Date |
2009 / March
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|---|---|
| Title | On a functional equation associated with the trapezoidal rule-II |
| Author | |
| Keyword | |
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| Pagination | 9-23 |
| Abstract | In this paper, we find the solution $f_1, f_2, f_3, f_4, f_5, g_1: \mathbb{R} \to \mathbb{R}$ of $f_1(y) - g_1(x) = (y - x) [f_2(x) + f_3 (sx + ty) + f_4(tx + sy) +
f_5(y)]$ for all real numbers $x$ and $y$. Here $s$ and $t$ are any two $a\ priori$ chosen real parameters. This functional equation is a generalization of a functional equation that arises in connection with the trapezoidal rule for the numerical evaluation of definite integrals and is a generalization of a functional equation studied in [10].
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| AMS Subject Classification |
39B22
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| Received |
2008-02-26
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| Accepted |
2008-03-05
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