... ψxδ>0 in the above Theorem 5.1, then we will obtain the Ulam-Hyers stabilityresult of Baker 31,Theorem3see also 37,Theorem7 for the linear equation 5.2.Hindawi Publishing CorporationFixed ... existence of a mappingc : G → Y such that the following hold.i c is a fixed point of J,thatis,w ◦c ◦ ηxcxhx, ∀x ∈ G. Ew,η The mapping c is the unique fixed point of J in the setF ... equation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 27, no. 4, pp. 222–224, 1941.2 T. Aoki, “On the stability of the linear transformation in Banach spaces,”...