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Hyperstability results for the general linear functional equation in non-Archimedean 2-Banach spaces

Let X be a 2-normed space over R, ℝ Y be a non-Archimedean 2-Banach space over non-Archimedean field K, r, s ℝ \ {0} , and R, S ∈ K \ {0}. In this paper, a short preface on non- Archimedean 2-Banach spaces (Y, ||,··||) is given. Then, we reformulate the Brzdek fixed point theorem in non-Archimedean...

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Main Authors: Shuja, Shujauddin, Embong, Ahmad Fadillah, Mohd. Ali, Nor Muhainiah
Format: Article
Language:English
Published: Universiti Kebangsaan Malaysia 2024
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/108921/1/AhmadFadillah2024_HyperstabilityResultsfortheGeneralLinear.pdf
http://eprints.utm.my/108921/
http://dx.doi.org/10.17576/jqma.2002.2024.04
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spelling my.utm.1089212024-12-15T06:02:28Z http://eprints.utm.my/108921/ Hyperstability results for the general linear functional equation in non-Archimedean 2-Banach spaces Shuja, Shujauddin Embong, Ahmad Fadillah Mohd. Ali, Nor Muhainiah QA Mathematics Let X be a 2-normed space over R, ℝ Y be a non-Archimedean 2-Banach space over non-Archimedean field K, r, s ℝ \ {0} , and R, S ∈ K \ {0}. In this paper, a short preface on non- Archimedean 2-Banach spaces (Y, ||,··||) is given. Then, we reformulate the Brzdek fixed point theorem in non-Archimedean 2-Banach spaces. Using the Brzdek fixed point method, we prove hyperstability results of the general linear functional equation h(rx + sy) = Rh(x) + Sh(y), x, y, ∈ X, in non-Archimedean 2-Banach spaces. In fact, under some natural assumptions on control function Y: X × X × Y → [0, ∞) , we show that every map satisfying ||h(rx + sy) - Rh(x) - Sh(y), z||* = ≤ y(x, y, z), x, y ∈ z, ∈ Y, is hyperstable in the class of functions h: X → Y. Universiti Kebangsaan Malaysia 2024-07 Article PeerReviewed application/pdf en http://eprints.utm.my/108921/1/AhmadFadillah2024_HyperstabilityResultsfortheGeneralLinear.pdf Shuja, Shujauddin and Embong, Ahmad Fadillah and Mohd. Ali, Nor Muhainiah (2024) Hyperstability results for the general linear functional equation in non-Archimedean 2-Banach spaces. Journal of Quality Measurement and Analysis, 20 (2). pp. 35-48. ISSN 1823-5670 http://dx.doi.org/10.17576/jqma.2002.2024.04 DOI:10.17576/jqma.2002.2024.04
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Shuja, Shujauddin
Embong, Ahmad Fadillah
Mohd. Ali, Nor Muhainiah
Hyperstability results for the general linear functional equation in non-Archimedean 2-Banach spaces
description Let X be a 2-normed space over R, ℝ Y be a non-Archimedean 2-Banach space over non-Archimedean field K, r, s ℝ \ {0} , and R, S ∈ K \ {0}. In this paper, a short preface on non- Archimedean 2-Banach spaces (Y, ||,··||) is given. Then, we reformulate the Brzdek fixed point theorem in non-Archimedean 2-Banach spaces. Using the Brzdek fixed point method, we prove hyperstability results of the general linear functional equation h(rx + sy) = Rh(x) + Sh(y), x, y, ∈ X, in non-Archimedean 2-Banach spaces. In fact, under some natural assumptions on control function Y: X × X × Y → [0, ∞) , we show that every map satisfying ||h(rx + sy) - Rh(x) - Sh(y), z||* = ≤ y(x, y, z), x, y ∈ z, ∈ Y, is hyperstable in the class of functions h: X → Y.
format Article
author Shuja, Shujauddin
Embong, Ahmad Fadillah
Mohd. Ali, Nor Muhainiah
author_facet Shuja, Shujauddin
Embong, Ahmad Fadillah
Mohd. Ali, Nor Muhainiah
author_sort Shuja, Shujauddin
title Hyperstability results for the general linear functional equation in non-Archimedean 2-Banach spaces
title_short Hyperstability results for the general linear functional equation in non-Archimedean 2-Banach spaces
title_full Hyperstability results for the general linear functional equation in non-Archimedean 2-Banach spaces
title_fullStr Hyperstability results for the general linear functional equation in non-Archimedean 2-Banach spaces
title_full_unstemmed Hyperstability results for the general linear functional equation in non-Archimedean 2-Banach spaces
title_sort hyperstability results for the general linear functional equation in non-archimedean 2-banach spaces
publisher Universiti Kebangsaan Malaysia
publishDate 2024
url http://eprints.utm.my/108921/1/AhmadFadillah2024_HyperstabilityResultsfortheGeneralLinear.pdf
http://eprints.utm.my/108921/
http://dx.doi.org/10.17576/jqma.2002.2024.04
_version_ 1818834066369150976
score 13.244413

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