On Hyers-Ulam-Rassias Stability and Hyperstability of Generalized Affine, Quadratic and Drygas Functional Equations

Abbas Najati (), Jafar Mohammadpour and Themistocles M. Rassias ()
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Abbas Najati: University of Mohaghegh Ardabili, Department of Mathematics, Faculty of Mathematical Sciences
Jafar Mohammadpour: University of Mohaghegh Ardabili, Department of Mathematics, Faculty of Mathematical Sciences
Themistocles M. Rassias: National Technical University of Athens, Department of Mathematics

Chapter 17 in Convex and Variational Analysis with Applications, 2026, pp 347-362 from Springer

Abstract: Abstract We investigate the Hyers-Ulam-Rassias stability and hyperstability of the functional equations $$\begin{aligned} f\left[ g(x+\lambda y)\right] &=f(x)+f(y),\\ f\left[ g(x+\lambda y)\right] +f\left[ g(x-\lambda y)\right] &=2f(x)+2\lambda ^2f(y),\\ f\left[ g(x+\lambda y)\right] +f\left[ g(x-\lambda y)\right] &=2f(x)+\lambda ^2[f(y)+f(-y)], \end{aligned}$$ f g ( x + λ y ) = f ( x ) + f ( y ) , f g ( x + λ y ) + f g ( x - λ y ) = 2 f ( x ) + 2 λ 2 f ( y ) , f g ( x + λ y ) + f g ( x - λ y ) = 2 f ( x ) + λ 2 [ f ( y ) + f ( - y ) ] , in Banach spaces.

Keywords: Hyperstability; Hyers-Ulam-Rassias stability; Cauchy functional equation; Quadratic function; Drygas function; Primary 39B82; 39B52; 39B72; 41A99 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-07860-5_17

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