On a Stability of Logarithmic‐Type Functional Equation in Schwartz Distributions

Jae-Young Chung

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: We prove the Hyers‐Ulam stability of the logarithmic functional equation of Heuvers and Kannappan f(x + y) − g(xy) − h(1/x + 1/y) = 0, x, y > 0, in both classical and distributional senses. As a classical sense, the Hyers‐Ulam stability of the inequality |f(x + y) − g(xy) − h(1/x + 1/y)| ≤ ϵ, x, y > 0 will be proved, where f, g, h : ℝ+ → ℂ. As a distributional analogue of the above inequality, the stability of inequality ∥u∘(x + y) − v∘(xy) − w∘(1/x + 1/y)∥ ≤ ϵ will be proved, where u, v, w ∈ 𝒟′(ℝ+) and ∘ denotes the pullback of distributions.

Date: 2012
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https://doi.org/10.1155/2012/435310

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:435310

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