On the summability methods of logarithmic type and the Berezin symbol

Authors: ULAŞ YAMANCI

Abstract: We prove by means of the Berezin symbols some theorems for the $\left( L\right) $-summability method for sequences and series. Also, we prove a new Tauberian type theorem for $\left( L\right) $-summability.

Keywords: $\left( L\right) $-summability, Berezin symbol, $\left( e\right) $-convergence, compact operator, Tauberian type theorem, Dirichlet space, diagonal operator

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