Orthogonality and Generalized Additive Mappings in Banach Modules

H. Azadi Kenary (), N. Sahami and M. H. Eghtesadifard
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H. Azadi Kenary: Islamic Azad University, Department of Mathematics, Beyza Branch
N. Sahami: Islamic Azad University, Department of Mathematics, Beyza Branch
M. H. Eghtesadifard: Yasouj University, Department of Mathematics

A chapter in Functional Equations and Ulam’s Problem, 2026, pp 41-54 from Springer

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

Keywords: Primary 39B55; 46S10; 47H10; 39B52; 47S10; 30G06; 46H25; 46L05; 12J25; Hyers-Ulam stability; Orthogonally Cauchy-Jensen additive functional equation; Fixed point; Non-Archimedean Banach module over C ∗ $$C^*$$ -algebra; Orthogonality space (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-08949-6_2

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