Generalised Ulam-Hyers stability of a &lt;i&gt;n&lt;/i&gt;-dimensional additive functional equation in two different methods

Arunkumar, M.; Agilan, P.; Ramamoorthy, Subramanian; Kumar, N. Mahesh

doi:10.1504/ijcaet.2020.107441

Cited by 3 publications

(1 citation statement)

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“…The detailed results of Ulam stability are explained in [21][22][23][24][25]. Different types of additive functional equations and their Ulam stability are addressed in [26][27][28][29][30]. Stability analysis is important in mathematics, with Ulam stability being particularly important for functional equations, differential equations, and integral equations.…”

Section: Introductionmentioning

confidence: 99%

Direct and Fixed-Point Stability–Instability of Additive Functional Equation in Banach and Quasi-Beta Normed Spaces

et al. 2022

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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.

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Section: Introductionmentioning

confidence: 99%

Direct and Fixed-Point Stability–Instability of Additive Functional Equation in Banach and Quasi-Beta Normed Spaces

et al. 2022

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Generalized Ulam-Hyers Stability of Complex Additive Functional Equation

Agilan

Vallinayagam

2019

J. Phys.: Conf. Ser.

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Stability Analysis of a New Class of Series Type Additive Functional Equation in Banach Spaces: Direct and Fixed Point Techniques

et al. 2023

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In this paper, the authors introduce two new classes of series type additive functional Equations (FEs). The first class of equations is derived from the sum of the squares of the alternative series and the second one is obtained from the sum of the cubes of the series. The solution of the FE is investigated using the principle of mathematical induction. The beauty of this method lies in the fact that it satisfies the property of the additive FE as well as the series. Banach spaces are one of the widely-used spaces that are very helpful to analyse the stability results of various FEs. The Banach space conditions have been applied and the stability results are established for both of the equations. Furthermore, the Banach Contraction principle and alternative of fixed point theorem are used to derive the stability results in a fixed point technique (FPT). The relationship between the FEs and both the series is established through the principle of mathematical induction in the Application section, which adds novelty to the derived results.

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Generalised Ulam-Hyers stability of a <i>n</i>-dimensional additive functional equation in two different methods

Cited by 3 publications

References 0 publications

Direct and Fixed-Point Stability–Instability of Additive Functional Equation in Banach and Quasi-Beta Normed Spaces

Direct and Fixed-Point Stability–Instability of Additive Functional Equation in Banach and Quasi-Beta Normed Spaces

Generalized Ulam-Hyers Stability of Complex Additive Functional Equation

Stability Analysis of a New Class of Series Type Additive Functional Equation in Banach Spaces: Direct and Fixed Point Techniques

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