The Hyers-Ulam stability for two functional equations in a single variable. (English) Zbl 1143.39015
The author applies the Luxemburg-Jung fixed point theorem to prove the Hyers-Ulam stability of the functional equations
\[ f(x)= F(x,f(\eta(x))) \quad\text{and}\quad (\mu\circ f\circ\eta)(x)= f(x). \]
The readers may also refer to the following papers for more information on this subject:
S.-M. Jung and T.-S. Kim [Bol. Soc. Mat. Mex., III. Ser. 12, No. 1, 51–57 (2006; Zbl 1133.39028)]; S.-M. Jung, T.-S. Kim and K.-S. Lee [Bull. Korean Math. Soc. 43, No. 3, 531–541 (2006; Zbl 1113.39031)]; S.-M. Jung [J. Math. Anal. Appl. 329, No. 2, 879–890 (2007), Fixed Point Theory Appl. 2007, Article ID 57064, 9 p. (2007; Zbl 1155.45005), Banach J. Math. Anal. 1, No. 2, 148–153, electronic only (2007; Zbl 1133.39027)].
\[ f(x)= F(x,f(\eta(x))) \quad\text{and}\quad (\mu\circ f\circ\eta)(x)= f(x). \]
The readers may also refer to the following papers for more information on this subject:
S.-M. Jung and T.-S. Kim [Bol. Soc. Mat. Mex., III. Ser. 12, No. 1, 51–57 (2006; Zbl 1133.39028)]; S.-M. Jung, T.-S. Kim and K.-S. Lee [Bull. Korean Math. Soc. 43, No. 3, 531–541 (2006; Zbl 1113.39031)]; S.-M. Jung [J. Math. Anal. Appl. 329, No. 2, 879–890 (2007), Fixed Point Theory Appl. 2007, Article ID 57064, 9 p. (2007; Zbl 1155.45005), Banach J. Math. Anal. 1, No. 2, 148–153, electronic only (2007; Zbl 1133.39027)].
Reviewer: Soon-Mo Jung (Chochiwon)
MSC:
| 39B82 | Stability, separation, extension, and related topics for functional equations |
