Abstract: Summability methods for ultraholomorphic classes in sectors, defined in terms of a strongly regular sequence , have been put forward by A. Lastra, S. Malek and the second author. We study several open questions related to the existence of kernels of summability constructed by means of analytic proximate orders. In particular, we give a simple condition that allows us to associate a proximate order with a strongly regular sequence. Under this assumption, and through the characterization of strongly regular sequences in terms of so-called regular variation, we show that the growth index defined by V. Thilliez and the order of quasianalyticity introduced by the second author are the same.

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