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On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions
Author
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-21
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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∈?'(ℝ+) and ∘ denotes the pullback of distributions.
American Psychological Association (APA)
Chung, Jae-Young. 2012. On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-472018
Modern Language Association (MLA)
Chung, Jae-Young. On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions. Abstract and Applied Analysis No. 2012 (2012), pp.1-15.
https://search.emarefa.net/detail/BIM-472018
American Medical Association (AMA)
Chung, Jae-Young. On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-15.
https://search.emarefa.net/detail/BIM-472018
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-472018