Hyers–Ulam stability of norm-additive functional equations via ( δ , ϵ ) $(\delta , \epsilon )$ -isometries
Abstract This research examines the Hyers–Ulam stability of norm-additive functional equations expressed as ∥ ξ ( g h − 1 ) ∥ = ∥ ξ ( g ) − ξ ( h ) ∥ , ∥ ξ ( g h ) ∥ = ∥ ξ ( g ) + ξ ( h ) ∥ , $$\begin{aligned}& \|\xi (gh^{-1})\|=\|\xi (g)-\xi (h)\|,\\& \|\xi (gh)\|=\|\xi (g)+\xi (h)\|, \end{...
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2025-01-01
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Series: | Journal of Inequalities and Applications |
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Online Access: | https://doi.org/10.1186/s13660-024-03233-y |
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author | Muhammad Sarfraz Jiang Zhou Yongjin Li |
author_facet | Muhammad Sarfraz Jiang Zhou Yongjin Li |
author_sort | Muhammad Sarfraz |
collection | DOAJ |
description | Abstract This research examines the Hyers–Ulam stability of norm-additive functional equations expressed as ∥ ξ ( g h − 1 ) ∥ = ∥ ξ ( g ) − ξ ( h ) ∥ , ∥ ξ ( g h ) ∥ = ∥ ξ ( g ) + ξ ( h ) ∥ , $$\begin{aligned}& \|\xi (gh^{-1})\|=\|\xi (g)-\xi (h)\|,\\& \|\xi (gh)\|=\|\xi (g)+\xi (h)\|, \end{aligned}$$ through the utilization of ( δ , ϵ ) $(\delta , \epsilon )$ -isometries. In this context, ξ : G → X $\xi : G \to X$ represents a surjective (δ-surjective) mapping, where G denotes noncommutative group (arbitrary group) and X signifies a Banach space (or a real Banach space). |
format | Article |
id | doaj-art-ae7eceda9b9a4c638346eaa28278840b |
institution | Kabale University |
issn | 1029-242X |
language | English |
publishDate | 2025-01-01 |
publisher | SpringerOpen |
record_format | Article |
series | Journal of Inequalities and Applications |
spelling | doaj-art-ae7eceda9b9a4c638346eaa28278840b2025-01-05T12:49:49ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-01-012025111610.1186/s13660-024-03233-yHyers–Ulam stability of norm-additive functional equations via ( δ , ϵ ) $(\delta , \epsilon )$ -isometriesMuhammad Sarfraz0Jiang Zhou1Yongjin Li2School of Mathematics and System Sciences, Xinjiang UniversitySchool of Mathematics and System Sciences, Xinjiang UniversitySchool of Mathematics, Sun Yat-sen UniversityAbstract This research examines the Hyers–Ulam stability of norm-additive functional equations expressed as ∥ ξ ( g h − 1 ) ∥ = ∥ ξ ( g ) − ξ ( h ) ∥ , ∥ ξ ( g h ) ∥ = ∥ ξ ( g ) + ξ ( h ) ∥ , $$\begin{aligned}& \|\xi (gh^{-1})\|=\|\xi (g)-\xi (h)\|,\\& \|\xi (gh)\|=\|\xi (g)+\xi (h)\|, \end{aligned}$$ through the utilization of ( δ , ϵ ) $(\delta , \epsilon )$ -isometries. In this context, ξ : G → X $\xi : G \to X$ represents a surjective (δ-surjective) mapping, where G denotes noncommutative group (arbitrary group) and X signifies a Banach space (or a real Banach space).https://doi.org/10.1186/s13660-024-03233-yIsometryHyers–Ulam stabilityBanach spaceNorm-additive functional equations |
spellingShingle | Muhammad Sarfraz Jiang Zhou Yongjin Li Hyers–Ulam stability of norm-additive functional equations via ( δ , ϵ ) $(\delta , \epsilon )$ -isometries Journal of Inequalities and Applications Isometry Hyers–Ulam stability Banach space Norm-additive functional equations |
title | Hyers–Ulam stability of norm-additive functional equations via ( δ , ϵ ) $(\delta , \epsilon )$ -isometries |
title_full | Hyers–Ulam stability of norm-additive functional equations via ( δ , ϵ ) $(\delta , \epsilon )$ -isometries |
title_fullStr | Hyers–Ulam stability of norm-additive functional equations via ( δ , ϵ ) $(\delta , \epsilon )$ -isometries |
title_full_unstemmed | Hyers–Ulam stability of norm-additive functional equations via ( δ , ϵ ) $(\delta , \epsilon )$ -isometries |
title_short | Hyers–Ulam stability of norm-additive functional equations via ( δ , ϵ ) $(\delta , \epsilon )$ -isometries |
title_sort | hyers ulam stability of norm additive functional equations via δ ϵ delta epsilon isometries |
topic | Isometry Hyers–Ulam stability Banach space Norm-additive functional equations |
url | https://doi.org/10.1186/s13660-024-03233-y |
work_keys_str_mv | AT muhammadsarfraz hyersulamstabilityofnormadditivefunctionalequationsviadedeltaepsilonisometries AT jiangzhou hyersulamstabilityofnormadditivefunctionalequationsviadedeltaepsilonisometries AT yongjinli hyersulamstabilityofnormadditivefunctionalequationsviadedeltaepsilonisometries |