an:05668700
Zbl 1189.39032
Popa, Dorian
A property of a functional inclusion connected with Hyers-Ulam stability
EN
J. Math. Inequal. 3, No. 4, 591-598 (2009).
00257813
2009
j
39B82 39B52 20L05
Hyers-Ulam stability; square-symmetric groupoid; functional inclusion
The author uses some ideas of \textit{D. Popa} [Math. Inequal. Appl. 7, No.~3, 419--428 (2004; Zbl 1058.39026)] and \textit{Z. P??les} [Publ. Math. 58, No.~4, 651--666 (2001; Zbl 0980.39022)] to prove that if \((X,*)\) is a square-symmetric divisible groupoid and \((Y,\diamond,d)\) is a complete metric bisymmetric divisible groupoid and \(F:X\to \mathcal{P}_0(Y)\) is a set valued map with the property \(F(x)\diamondsuit F(Y)\subseteq F(x*y)\), then under certain conditions there exists a unique selection \( f:X\to Y\) of \(F\) such that \(f(x)\diamond f(y)=f(x*y)\).
Maryam Amyari (Mashhad)
Zbl 1058.39026; Zbl 0980.39022