Hyperstability of Cauchy and Jensen functional equations in 2-normed spaces

In this article, with simple and short proofs without applying fixed point theorems, some hyperstability results corresponding to the functional equations of Cauchy and Jensen are presented in 2-normed spaces. We also obtain some results on hyperstability for the general linear functional equation f...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2024; no. 1; pp. 49 - 13
Main Authors Najati, Abbas, Yengejeh, Yavar Khedmati, Tamilvanan, Kandhasamy, Kabeto, Masho Jima
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 03.04.2024
Springer Nature B.V
SpringerOpen
Subjects
2-normed space
Analysis
Applications of Mathematics
Cauchy functional equation
Fixed points (mathematics)
Functional equations
General linear functional equation
Hyperstability
Jensen functional equation
Mathematical analysis
Mathematics
Mathematics and Statistics
Theorems
Hyperstability
Cauchy functional equation
39B62
General linear functional equation
2-normed space
Jensen functional equation
46B20
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Summary:In this article, with simple and short proofs without applying fixed point theorems, some hyperstability results corresponding to the functional equations of Cauchy and Jensen are presented in 2-normed spaces. We also obtain some results on hyperstability for the general linear functional equation f ( a x + b y ) = A f ( x ) + B f ( y ) + C .
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-024-03116-2