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Keywords = quasi-beta normed spaces

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28 pages, 360 KB  
Article
Direct and Fixed-Point Stability–Instability of Additive Functional Equation in Banach and Quasi-Beta Normed Spaces
by Agilan Pasupathi, Julietraja Konsalraj, Nahid Fatima, Vallinayagam Velusamy, Nabil Mlaiki and Nizar Souayah
Symmetry 2022, 14(8), 1700; https://doi.org/10.3390/sym14081700 - 16 Aug 2022
Cited by 9 | Viewed by 1655
Abstract
Over the last few decades, a certain interesting class of functional equations were developed while obtaining the generating functions of many system distributions. This class of equations has numerous applications in many modern disciplines such as wireless networks and communications. The Ulam stability [...] Read more.
Over the last few decades, a certain interesting class of functional equations were developed while obtaining the generating functions of many system distributions. This class of equations has numerous applications in many modern disciplines such as wireless networks and communications. The Ulam stability theorem can be applied to numerous functional equations in investigating the stability when approximated in Banach spaces, Banach algebra, and so on. The main focus of this study is to analyse the relationship between functional equations, Hyers–Ulam–Rassias stability, Banach space, quasi-beta normed spaces, and fixed-point theory in depth. The significance of this work is the incorporation of the stability of the generalised additive functional equation in Banach space and quasi-beta normed spaces by employing concrete techniques like direct and fixed-point theory methods. They are powerful tools for narrowing down the mathematical models that describe a wide range of events. Some classes of functional equations, in particular, have lately emerged from a variety of applications, such as Fourier transforms and the Laplace transforms. This study uses linear transformation to explain our functional equations while providing suitable examples. Full article
(This article belongs to the Special Issue The Qualitative Theory of Functional Differential Equations and their Applications)
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