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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(η(x)))and(μfη)(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)].

MSC:
39B82Stability, separation, extension, and related topics