Stability of an Alternative Functional Equation Related to the Quadratic Equation

Paper Details

Authors: Srisawat C.; Trachoo K.

DOI: 10.28924/2291-8639-24-2026-102

Journal: International Journal of Analysis and Applications

Year: 2026

Publisher: Etamaths Publishing

Document Type: Article

Open Access: All Open Access; Gold Open Access

Cited by: 0

Abstract

Given a rational number α ≠ ±2, a criterion is established for the existence of the general solution to the alternative quadratic functional equation of the form (Formula presented), where f is a mapping from an abelian group (G, ·) to a uniquely divisible abelian group (H, +). Subsequently, the Hyers-Ulam stability of this equation is proved for mappings from an abelian group to a Banach space, provided that α ≠ {0, ± 21, ±1, ±2} is a rational number. © 2026 the author(s).

Keywords

alternative functional equation, Hyers-Ulam stability; quadratic functional equation

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