Additive functional equation and inequality are stable in Banach space and its applications

Arunkumar, M.; Agilan, P.

doi:10.26637/mjm101/002

Cited by 6 publications

(1 citation statement)

References 16 publications

(18 reference statements)

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“…The historical background of the stability of functional equations and literature survey has been explained in the cited references (see [12][13][14][15][16][17][18][19][20]). 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].…”

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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