Abstract
Curtis Outlaw and C. W. Groetsclh [4] have recently shown that if T is an asymptotically convergent continuous linear self-mapping of a Banach space E, and if f is in the range of I-T, and 0 E is a continuous linear operator, and fEE. For O 1, and for n>1, anj=(j_ )Xn'-(1 -X)j-l for 1 n. It is easily seen that AX is a lower-triangular, nonnegative, inifinite matrix with each row-sum equal to one and each column-limit equal to zero. For n > 1 we have the real polynomial a(t) defined by
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