On Ulam Stability and Hyperstability of Functional Equations in Banach Spaces and 2-Banach Spaces

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

A chapter in Functional Equations and Ulam’s Problem, 2026, pp 369-392 from Springer

Abstract: Abstract We investigate the Ulam stability and hyperstability of the functional equations f x − y 2 + z + f y − z 2 + x + f z − x 2 + y = f ( x + y + z ) , f x − y 2 + z + f y − z 2 + x + f z − x 2 + y = f ( x ) + f ( y ) + f ( z ) , $$\displaystyle \begin {array}{l} f\left (\frac {x-y}{2}+z\right )+ f\left (\frac {y-z}{2}+x\right )+ f\left (\frac {z-x}{2}+y\right )=f(x+y+z),\\ f\left (\frac {x-y}{2}+z\right )+ f\left (\frac {y-z}{2}+x\right )+ f\left (\frac {z-x}{2}+y\right )=f(x)+f(y)+f(z), \end {array} $$ in Banach spaces and 2-Banach spaces.

Keywords: Hyers-Ulam stability; Hyperstability; Cauchy functional equation; 2-Normed space; 2-Banach space; Primary 39B82; 39B52; 39B72 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-08949-6_18

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