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On the Superstability of Lobačevskiǐ’s Functional Equations with Involution
Joint Authors
Lee, Bogeun
Ha, Misuk
Chung, Jae-Young
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-04-03
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
Let G be a uniquely 2-divisible commutative group and let f,g:G→C and σ:G→G be an involution.
In this paper, generalizing the superstability of Lobačevskiǐ’s functional equation, we consider f(x+σy)/22-g(x)f(y)≤ψ(x) or ψ(y) for all x,y∈G, where ψ:G→R+.
As a direct consequence, we find a weaker condition for the functions f satisfying the Lobačevskiǐ functional inequality to be unbounded, which refines the result of Găvrută and shows the behaviors of bounded functions satisfying the inequality.
We also give various examples with explicit involutions on Euclidean space.
American Psychological Association (APA)
Chung, Jae-Young& Lee, Bogeun& Ha, Misuk. 2016. On the Superstability of Lobačevskiǐ’s Functional Equations with Involution. Journal of Function Spaces،Vol. 2016, no. 2016, pp.1-7.
https://search.emarefa.net/detail/BIM-1108555
Modern Language Association (MLA)
Chung, Jae-Young…[et al.]. On the Superstability of Lobačevskiǐ’s Functional Equations with Involution. Journal of Function Spaces No. 2016 (2016), pp.1-7.
https://search.emarefa.net/detail/BIM-1108555
American Medical Association (AMA)
Chung, Jae-Young& Lee, Bogeun& Ha, Misuk. On the Superstability of Lobačevskiǐ’s Functional Equations with Involution. Journal of Function Spaces. 2016. Vol. 2016, no. 2016, pp.1-7.
https://search.emarefa.net/detail/BIM-1108555
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1108555