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<p>In the current study, we represent a multi-Drygas mapping (defined by EL-Fassi et al. as a system of the multi-Drygas functional equations) as an equation. We also portray that a multi-Drygas mapping under odd or even condition in each variable can be reduced to multi-Jensen, multi-quadratic and multi-Jensen-quadratic. Moreover, we prove the Găvruţa and Hyers stability (without zero condition) of the multi-Drygas mappings via a known fixed point approach due to Brzdȩk. These results show that we can remove the condition zero condition which is applied in the work of Dehghanian et al. [<CitationRef CitationID="CR14">14</CitationRef>] for Hyers stability. As a result, we establish the Hyers stability of the multi-quadratic mappings. Furthermore, we investigate the stability (as pointwise) of multi-Drygas mappings on a restricted domain. Finally, some concrete examples for the validity of our stability result on the restricted domain, are illustrated.</p>

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Multivariable mappings associated with the Drygas functional equation and a fixed point approach

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Abasalt Bodaghi,
  • Mehdi Dehghanian,
  • Yamin Sayyari

摘要

In the current study, we represent a multi-Drygas mapping (defined by EL-Fassi et al. as a system of the multi-Drygas functional equations) as an equation. We also portray that a multi-Drygas mapping under odd or even condition in each variable can be reduced to multi-Jensen, multi-quadratic and multi-Jensen-quadratic. Moreover, we prove the Găvruţa and Hyers stability (without zero condition) of the multi-Drygas mappings via a known fixed point approach due to Brzdȩk. These results show that we can remove the condition zero condition which is applied in the work of Dehghanian et al. [14] for Hyers stability. As a result, we establish the Hyers stability of the multi-quadratic mappings. Furthermore, we investigate the stability (as pointwise) of multi-Drygas mappings on a restricted domain. Finally, some concrete examples for the validity of our stability result on the restricted domain, are illustrated.