... 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 ... facts:1 the contraction property of a Schr¨oder-type operator J,2 the first two approximations, f and Jf,tobeatafinite distance,3 they force the fixed point of J to be a solution of the initial ... application of our result for 1.8, the stability for the following generalized functionalequation of the square root spiralfp−1pxk fxhx1.9is obtained.Thereafter, we present the...