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Hyers-Ulam-Rassias stability of a quadratic functional equation
Tiberiu Trif 대한수학회 2003 대한수학회보 Vol.40 No.2
In this paper we deal with the quadratic functional equationbegin{eqnarray*}& & n^2binom{n-2}{k-2}fleft(frac{x_1+cdots+x_n}{n}right)+binom{n-2}{k-1}sum_{i=1}^n f(x_i) & =& k^2sum_{1leq i_1<cdots<i_kleq n}fleft(frac{x_{i_1}+cdots+x_{i_k}}{k}right),end{eqnarray*}deriving from an inequality of T. Popoviciu for convex functions. We solve this functional equation by proving thatits solutions are the polynomials of degree at most two. Likewise, we investigate its stability in the spirit ofHyers, Ulam, and Rassias.
HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION
Trif, Tiberiu Korean Mathematical Society 2003 대한수학회보 Vol.40 No.2
In this paper we deal With the quadratic functional equation (equation omitted) deriving from an inequality of T. Popoviciu for convex functions. We solve this functional equation by proving that its solutions we the polynomials of degree at most two. Likewise, we investigate its stability in the spirit of Hyers, Ulam, and Rassias.