On the Asymptotic Behaviors Associated with the Davison Functional Equation
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Authors: M. A. TAREEGHEE, A. NAJATI AND J-H. BAE
DOI: 10.46793/KgJMat2605.777T
Abstract:
We prove the Hyers-Ulam stability of the Davison functional equation
for a class of mappings from a normed algebra ???? (with a unit element 1) into a
Banach space ℬ, on the restricted domain 
,
where d > 0 is a constant. As a result, we obtain some asymptotic behaviors of
Davison mappings. In addition, we obtain the corollary that for every mapping g
from a normed algebra ???? into a normed space ℬ, and for all positive real numbers
r,s, one of the following two conditions must be valid:
or
Keywords:
Hyers-Ulam stability, Davison functional equation, asymptotic behavior.
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