On the Stability of Some Functional Equations and s-Functional Inequalities

B. Noori (), M. B. Moghimi (), A. Najati () and Themistocles M. Rassias ()
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B. Noori: University of Mohaghegh Ardabili, Faculty of Sciences, Department of Mathematics
M. B. Moghimi: University of Mohaghegh Ardabili, Faculty of Sciences, Department of Mathematics
A. Najati: University of Mohaghegh Ardabili, Faculty of Sciences, Department of Mathematics
Themistocles M. Rassias: National Technical University of Athens, Department of Mathematics

A chapter in Approximation Theory and Analytic Inequalities, 2021, pp 339-353 from Springer

Abstract: Abstract In this work, the Hyers–Ulam type stability and the hyperstability of the following functional equations f ( x + y ) + f ( x − y ) = f ( 2 x ) + f ( y ) + f ( − y ) , f ( a x + y ) + f ( a x − y ) = f ( a x ) + a f ( x ) , f ( a x + y ) + f ( a x − y ) = f ( a x ) + a f ( x ) + f ( y ) + f ( − y ) $$\displaystyle \begin {aligned}{} f(x+y)+f(x-y)&=f(2x)+f(y)+f(-y),\\ f(ax+y)+f(ax-y)&=f(ax)+af(x),\\ f(ax+y)+f(ax-y)&=f(ax)+af(x)+f(y)+f(-y) \end {aligned} $$ are proved. We also introduce and solve some s-functional inequalities, and we prove their Hyers–Ulam stabilities.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-60622-0_18

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DOI: 10.1007/978-3-030-60622-0_18

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