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On a functional equation associated with the trapezoidal rule-II
by Prasanna K. Sahoo  

Vol. 4 No. 1 (2009) P.9~P.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].


KEYWORDS
Additive map, functional equation, trapezoidal rule

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 39B22

MILESTONES

Received: 2007-06-27
Revised : 2008-02-26
Accepted: 2008-03-05


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