Abstract
A well-known theorem due to Littlewood (1911) and Andersen (1921) tells us that the family of summability methods consisting of the Abel method and all Cesàro methods C α , α > −1, is convex. In this paper we prove that this theorem remains true if we replace the Abel method and the Cesàro methods by the Borel method and the Euler-Knopp methods of positive order, respectively. Furthermore, we give some variants of this result in case of other circle methods of summability.
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