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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: {\it S.-M. Jung} and {\it T.-S. Kim} [Bol. Soc. Mat. Mex., III. Ser. 12, No. 1, 51--57 (2006; Zbl 1133.39028)]; {\it S.-M. Jung}, {\it T.-S. Kim} and {\it K.-S. Lee} [Bull. Korean Math. Soc. 43, No. 3, 531--541 (2006; Zbl 1113.39031)]; {\it 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)].

##### MSC:
 39B82 Stability, separation, extension, and related topics
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