Abstract and Applied Analysis

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

Jae-Young Chung

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Abstract

We prove the Hyers-Ulam stability of the logarithmic functional equation of Heuvers and Kannappan f ( x + y ) - g ( x y ) - 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 ( x y ) - h ( 1 / x + 1 / y ) | ϵ ,    x , y > 0 will be proved, where f , g , h : + . As a distributional analogue of the above inequality, the stability of inequality u ( x + y ) - v ( x y ) - w ( 1 / x + 1 / y ) ϵ will be proved, where u , v , w 𝒟 ' ( + ) and denotes the pullback of distributions.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 435310, 15 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475944

Digital Object Identifier
doi:10.1155/2012/435310

Mathematical Reviews number (MathSciNet)
MR2999887

Zentralblatt MATH identifier
1259.39020

Citation

Chung, Jae-Young. On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions. Abstr. Appl. Anal. 2012 (2012), Article ID 435310, 15 pages. doi:10.1155/2012/435310. https://projecteuclid.org/euclid.aaa/1364475944


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