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Using the fixed point method, we prove the Hyers-Ulam stability of the following generalized Jensen functional equation \(\displaystyle f\left (\frac {\sum _{i=1}^n x_i}{n}\right )+\sum _{i=1}^n f\left (\frac {\sum _{i=1,i\neq j}^n x_i -(n-1)x_j}{n}\right )=f(x_1)\quad (n\geq 2) \) in Banach modules over a unital \(C^*\) -algebra and in non-Archimedean Banach modules over a unital \(C^*\) -algebra associated with the orthogonally Jensen functional equation.

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Orthogonality and Generalized Additive Mappings in Banach Modules

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  • 发表日期：

    2026年

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  • H. Azadi Kenary,
  • N. Sahami,
  • M. H. Eghtesadifard

摘要

Using the fixed point method, we prove the Hyers-Ulam stability of the following generalized Jensen functional equation \(\displaystyle f\left (\frac {\sum _{i=1}^n x_i}{n}\right )+\sum _{i=1}^n f\left (\frac {\sum _{i=1,i\neq j}^n x_i -(n-1)x_j}{n}\right )=f(x_1)\quad (n\geq 2) \) in Banach modules over a unital \(C^*\) -algebra and in non-Archimedean Banach modules over a unital \(C^*\) -algebra associated with the orthogonally Jensen functional equation.