Hyperstability of the General Linear Functional Equation in Non-Archimedean Banach Spaces

Let be a normed space over , be a non-Archimedean Banach space over a non-Archimedean non-trivial field and be constants such that, and . In this paper, some preliminaries on non-Archimedean Banach spaces and the concept of hyperstability are presented. Next, the well-known fixed point method [ 7 ,...

Full description

Saved in:
Bibliographic Details
Published in:P-adic numbers, ultrametric analysis, and applications ultrametric analysis, and applications, 2024-03, Vol.16 (1), p.70-81
Main Authors: Shuja, Shujauddin, Embong, Ahmad F., Ali, Nor M. M.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Algebra
Banach spaces
Fixed points (mathematics)
Functional equations
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let be a normed space over , be a non-Archimedean Banach space over a non-Archimedean non-trivial field and be constants such that, and . In this paper, some preliminaries on non-Archimedean Banach spaces and the concept of hyperstability are presented. Next, the well-known fixed point method [ 7 , Theorem1] is reformulated in non-Archimedean Banach spaces. Using this method, we prove that the general linear functional equation is hyperstable in the class of functions . In fact, by exerting some natural assumptions on control function , we show that the map that satisfies the inequality , is a solution to general linear functional equation for every . Finally, this paper concludes with some consequences of the results.
ISSN:2070-0466
2070-0474
DOI:10.1134/S2070046624010060