Average approximations and moments of measures (Q1578425)

Here the author investigates average approximation of infinite dimensional mappings and related problems connected with moments of measures. He constructs an example relating to unsolvability of approximation on the average of the identity mapping that confirms a conjecture of \textit{J. F. Traub} and \textit{A. G. Werschulz} [Math. Intell. 16, No. 2, 42-48 (1994; Zbl 0832.47010)]. Several positive results concerning average approximations of Banach space valued mappings are also obtained and some related existing results are improved upon.