On the Superstability of Lobačevskiǐ’s Functional Equations with Involution
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 condi...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2016-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/1036094 |
| id |
doaj-3d111a5835a84346bf5443a2b6d5963b |
|---|---|
| record_format |
Article |
| spelling |
doaj-3d111a5835a84346bf5443a2b6d5963b2020-11-24T23:47:24ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/10360941036094On the Superstability of Lobačevskiǐ’s Functional Equations with InvolutionJaeyoung Chung0Bogeun Lee1Misuk Ha2Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of KoreaDepartment of Mathematics, Jeonbuk National University, Jeonju 561-756, Republic of KoreaDepartment of Mathematics, Jeonbuk National University, Jeonju 561-756, Republic of KoreaLet 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.http://dx.doi.org/10.1155/2016/1036094 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jaeyoung Chung Bogeun Lee Misuk Ha |
| spellingShingle |
Jaeyoung Chung Bogeun Lee Misuk Ha On the Superstability of Lobačevskiǐ’s Functional Equations with Involution Journal of Function Spaces |
| author_facet |
Jaeyoung Chung Bogeun Lee Misuk Ha |
| author_sort |
Jaeyoung Chung |
| title |
On the Superstability of Lobačevskiǐ’s Functional Equations with Involution |
| title_short |
On the Superstability of Lobačevskiǐ’s Functional Equations with Involution |
| title_full |
On the Superstability of Lobačevskiǐ’s Functional Equations with Involution |
| title_fullStr |
On the Superstability of Lobačevskiǐ’s Functional Equations with Involution |
| title_full_unstemmed |
On the Superstability of Lobačevskiǐ’s Functional Equations with Involution |
| title_sort |
on the superstability of lobačevskiǐ’s functional equations with involution |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces |
| issn |
2314-8896 2314-8888 |
| publishDate |
2016-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2016/1036094 |
| work_keys_str_mv |
AT jaeyoungchung onthesuperstabilityoflobacevskiisfunctionalequationswithinvolution AT bogeunlee onthesuperstabilityoflobacevskiisfunctionalequationswithinvolution AT misukha onthesuperstabilityoflobacevskiisfunctionalequationswithinvolution |
| _version_ |
1725489863190380544 |