Functional inequalities in non-Archimedean Banach spaces

In this work, we prove the generalized Hyers–Ulam stability of the following functional inequality: ‖ f ( x ) + f ( y ) + f ( z ) ‖ ≤ ‖ k f ( x + y + z k ) ‖ , | k | < | 3 | , in non-Archimedean Banach spaces.

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Bibliographic Details
Published in:Applied mathematics letters 2010-10, Vol.23 (10), p.1238-1242
Main Authors: Cho, Yeol Je, Park, Choonkil, Saadati, Reza
Format: Article
Language:English
Subjects:
Difference and functional equations, recurrence relations
Exact sciences and technology
Finite differences and functional equations
Functional analysis
Functional inequality
Generalized Hyers–Ulam stability
Jordan–von Neumann functional equation
Mathematical analysis
Mathematics
Non-Archimedean Banach space
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
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Summary:In this work, we prove the generalized Hyers–Ulam stability of the following functional inequality: ‖ f ( x ) + f ( y ) + f ( z ) ‖ ≤ ‖ k f ( x + y + z k ) ‖ , | k | < | 3 | , in non-Archimedean Banach spaces.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2010.06.005