What question did this study set out to answer?

The aim is to investigate the generalized Hyers–Ulam stability of a multi-variable additive-quadratic functional equation.

July 12, 2026MathematicsOpen Access

Hyers–Ulam Stability of a Multi-Variable Additive-Quadratic Functional Equation

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Randomized trial investigates Hyers–Ulam stability in Banach spaces, highlighting critical analytical challenges.

The aim is to investigate the generalized Hyers–Ulam stability of a multi-variable additive-quadratic functional equation.
Proved a structural equivalence theorem between multivariable and classical systems.
Utilized direct constructive aggregation method and generalized metric fixed-point alternative.
Constructed a counterexample demonstrating instability at a critical exponent threshold p=3.
Established comprehensive stability results in the multivariable framework.
Proved the inherent instability of the system at the critical exponent threshold p=3.

Bae et al. (2026) studied this question.

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