On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions
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,...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/435310 |
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| author | Jae-Young Chung |
| author_facet | Jae-Young Chung |
| author_sort | Jae-Young Chung |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e3058f8df09747bca913c74138a36dd0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e3058f8df09747bca913c74138a36dd02025-02-03T01:22:05ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/435310435310On a Stability of Logarithmic-Type Functional Equation in Schwartz DistributionsJae-Young Chung0Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of KoreaWe 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.http://dx.doi.org/10.1155/2012/435310 |
| spellingShingle | Jae-Young Chung On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions Abstract and Applied Analysis |
| title | On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions |
| title_full | On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions |
| title_fullStr | On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions |
| title_full_unstemmed | On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions |
| title_short | On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions |
| title_sort | on a stability of logarithmic type functional equation in schwartz distributions |
| url | http://dx.doi.org/10.1155/2012/435310 |
| work_keys_str_mv | AT jaeyoungchung onastabilityoflogarithmictypefunctionalequationinschwartzdistributions |