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Stability of Coupled Biquadratic Functional Equations Involving Four Mappings in Non-Archimedean Normed Spaces

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  • Janyarak Tongsomporn
  • Sorravit Phonrakkhet

Abstract

This paper investigates the Hyers–Ulam stability of a class of generalized biquadratic functional equations involving four unknown mappings in non-Archimedean normed spaces. We analyze a coupled system that simultaneously incorporates additive, quadratic, additive–quadratic, and quadratic–additive behaviors, thereby capturing both symmetric and asymmetric interactions among the variables. By exploiting the ultrametric structure inherent in non-Archimedean normed spaces, we establish the existence and uniqueness of approximating solutions, together with stability bounds. Furthermore, a known stability result for biquadratic functional equations is recovered as a corollary of the main theorem.

Suggested Citation

  • Janyarak Tongsomporn & Sorravit Phonrakkhet, 2026. "Stability of Coupled Biquadratic Functional Equations Involving Four Mappings in Non-Archimedean Normed Spaces," Journal of Mathematics, Hindawi, vol. 2026, pages 1-16, August.
    • Handle: RePEc:hin:jjmath:4930323
    DOI: 10.1155/jom/4930323
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