The Best Ulam Constant of the Fréchet Functional Equation

Irina Opraie, Dorian Popa and Liana Timboş
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Irina Opraie: Department of Mathematics, Technical University of Cluj-Napoca, G. Bariţiu No. 25, 400027 Cluj-Napoca, Romania
Dorian Popa: Department of Mathematics, Technical University of Cluj-Napoca, G. Bariţiu No. 25, 400027 Cluj-Napoca, Romania
Liana Timboş: Department of Mathematics, Technical University of Cluj-Napoca, G. Bariţiu No. 25, 400027 Cluj-Napoca, Romania

Mathematics, 2022, vol. 10, issue 10, 1-10

Abstract: In this paper, we prove the Ulam stability of the Fréchet functional equation f ( x + y + z ) + f ( x ) + f ( y ) + f ( z ) = f ( x + y ) + f ( y + z ) + f ( z + x ) arising from the characterization of inner product spaces and we determine its best Ulam constant. Using this result, we give a stability result for a pexiderized version of the Fréchet functional equation.

Keywords: Fréchet equation; Ulam stability; best constant (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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