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On positive answer to El-Fassi’s question related to hyperstability of the general radical quintic functional equation in quasi-β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-Banach spaces

Authors
  • Van Dung, Nguyen1
  • Sintunavarat, Wutiphol2
  • 1 Dong Thap University, Cao Lanh, Dong Thap, Vietnam , Cao Lanh (Vietnam)
  • 2 Thammasat University Rangsit Center, Pathumthani, 12120, Thailand , Pathumthani (Thailand)
Type
Published Article
Journal
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Publisher
Springer International Publishing
Publication Date
Aug 10, 2021
Volume
115
Issue
4
Identifiers
DOI: 10.1007/s13398-021-01111-6
Source
Springer Nature
Keywords
Disciplines
  • Original Paper
License
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Abstract

In this paper, we are interested to study El-Fassi’s question on hyperstability of the general radical quintic functional equation in quasi-β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-Banach spaces in [6]. First, we give some counterexamples to show that the hyperstability of a given functional equation does not occur. Then, by using the (β,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\beta ,p)$$\end{document}-normalization theorem, we prove the stability for the general radical quintic functional equation in quasi-β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-Banach spaces.

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