TY - JOUR

T1 - Hyers - Ulam stability of the Cauchy functional equation on square-symmetric groupoids

AU - Páles, Zsolt

PY - 2001/12/1

Y1 - 2001/12/1

N2 - The stability of the functional equation f (x ◇ y)= f (x) * f (y) (x, y ∈ X) is investigated, where f : X → Y and ◇, * are square-symmetric operations on the sets X and Y, respectively. The results presented include and generalize the classical theorem of Hyers obtained on the stability of the Cauchy functional equation in 1941.

AB - The stability of the functional equation f (x ◇ y)= f (x) * f (y) (x, y ∈ X) is investigated, where f : X → Y and ◇, * are square-symmetric operations on the sets X and Y, respectively. The results presented include and generalize the classical theorem of Hyers obtained on the stability of the Cauchy functional equation in 1941.

KW - Cauchy functional equation

KW - Hyers - Ulam stability

KW - Square-symmetric groupoid

UR - http://www.scopus.com/inward/record.url?scp=0035661343&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035661343&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035661343

VL - 58

SP - 651

EP - 666

JO - Publicationes Mathematicae

JF - Publicationes Mathematicae

SN - 0033-3883

IS - 4

ER -