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An n-dimensional mixed-type additive and quadratic functional equation and its stability

Wanchitra Towanlong, Paisan Nakmahachalasint^*

 
ABSTRACT:     We determine the general solution of the n-dimensional mixed-type additive and quadratic functional equation, 2f(∑ⁿ_i=1x_i) +∑_{1≤ i,j ≤ n, i≠ j}f(x_i−x_j) = (n+1)∑ⁿ_i=1f(x_i)+(n−1)∑ⁿ_i=1f(−x_i), where n>1, and investigate its general stability.

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* Corresponding author, E-mail: paisan.n@chula.ac.th

Received 24 Oct 2008, Accepted 20 Oct 2009