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<p>In this paper, we introduce the notion of generalized biderivations on quasi-Banach algebras, which is a natural generalization of ordinary biderivations. The study focuses on the hyperstability of generalized biderivations on quasi-Banach algebras using direct method (Hyers method) and fixed point (FP) method. Specifically, we use these methods to prove that every approximate (in some sense) generalized biderivation on a quasi-Banach algebra is actually an exact generalized biderivation. As applications, we give an extension and generalization of some of the main results obtained in Park et al. (J. Fixed Point Theory Appl. 22: 27, 2020).</p>

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The hyperstability of generalized biderivations on quasi-Banach algebras

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • Jawad Boutarfass,
  • Iz-iddine EL-Fassi,
  • Lahcen Oukhtite

摘要

In this paper, we introduce the notion of generalized biderivations on quasi-Banach algebras, which is a natural generalization of ordinary biderivations. The study focuses on the hyperstability of generalized biderivations on quasi-Banach algebras using direct method (Hyers method) and fixed point (FP) method. Specifically, we use these methods to prove that every approximate (in some sense) generalized biderivation on a quasi-Banach algebra is actually an exact generalized biderivation. As applications, we give an extension and generalization of some of the main results obtained in Park et al. (J. Fixed Point Theory Appl. 22: 27, 2020).