Abstract
In this paper, using the fixed-point and direct methods, we prove the Hyers-Ulam stability of the following m-Appolonius type functional equation: ∑i=1mf(x−xi)=mf(z−1m2∑i=1mxi)−1m∑1≤i<j≤mf(xi+xj), where m is a natural number greater than 1, in random normed spaces.
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