Deferred logarithmic summability and its applications to Tauberian theory

Abstract

In this paper, we define and introduce deferred logarithmic transformations, which are more general and effective than well-known transformations. Additionally, we provide several inclusion theorems and illustrative examples. We investigate the limiting behavior of deferred logarithmic moving averages of numerical sequences. We also present necessary and sufficient Tauberian conditions under which convergence of a sequence or its certain subsequences  follows from its deferred logarithmic summability. As a result, the method and theory developed in this paper may contribute to obtaining more interesting and useful results in relation to other advanced summability methods and to extending these findings to additional areas of research.