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On Hyers–Ulam Stability of Cauchy and Wilson Equations
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Abstract
We study the Hyers–Ulam stability problem for the Cauchy and Wilson integral equations
where ???? is a topological group, ????, ???? : ???? → ℂ are continuous functions, μ is a complex measure with compact support and σ is a continuous involution of ????. The result obtained in this paper are natural extensions of the previous works concerning the Hyers–Ulam stability of the Cauchy and Wilson functional equations done in the particular case of μ=δe
: The Dirac measure concentrated at the identity element of ????.
Title: On Hyers–Ulam Stability of Cauchy and Wilson Equations
Description:
Abstract
We study the Hyers–Ulam stability problem for the Cauchy and Wilson integral equations
where ???? is a topological group, ????, ???? : ???? → ℂ are continuous functions, μ is a complex measure with compact support and σ is a continuous involution of ????.
The result obtained in this paper are natural extensions of the previous works concerning the Hyers–Ulam stability of the Cauchy and Wilson functional equations done in the particular case of μ=δe
: The Dirac measure concentrated at the identity element of ????.
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