Hyers-Ulam stability of functional equations with parameters
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Abstract
This paper explores the Hyers-Ulam stability of parameterized generalized Jensen additive and quadratic functional equations in \(\beta\)-homogeneous \(F\)-spaces, showing that approximately satisfying mappings have a unique exact approximating counterpart within a specific bound. The corresponding stability theorems are established with estimates. The results extend existing stability results to the parameterized case, enrich the theory of functional equations in \(\beta\)-homogeneous \(F\)-spaces, and provide a concise proof approach for similar equations.
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