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{...

Full description

Saved in:
Bibliographic Details
Main Authors: Muhammad Sarfraz, Jiang Zhou, Yongjin Li
Format: Article
Language:English
Published: SpringerOpen 2025-01-01
Series:Journal of Inequalities and Applications
Subjects:
Online Access:https://doi.org/10.1186/s13660-024-03233-y
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1841559024308322304
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