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Demonstrates stability results of quadratic ∗-derivations in ρ-complete convex n-modular ∗-algebras, suggesting a general solution.
In this paper, we introduce the following quadratic functional equation: ∑i=1m−1ii+1f∑j=1ixji−xi+1+1mf∑i=1mxi=∑i=1mf(xi) which is derived from a geometric median identity in the Euclidean plane. Then, we find a general solution to the quadratic functional equation and prove the stability results of the quadratic ∗-derivations in ρ-complete convex n-modular ∗-algebras.
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Kim et al. (2026) studied this question.
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