Some Tauberian theorems for the statistical limit and statistical summability of ℓ(k) mean of functions

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If a function s has a limit ? at ?, then the statistical limit of function s exists and equals ?. However, the converse implication is not always true. In this paper, we present Tauberian conditions on general logarithmic control modulo that allow us to obtain the existence of ordinary limit of a function that has statistical limit ?. Additionally, we introduce the statistical summability of ?(k) mean of functions for each nonnegative integer k and provide conditions for Tauberian theorems. Our theorems generalize some well-known Tauberian theorems in the literature.