Statistical Deferred Cesaro Summability and Its Applications to Tauberian Theory

Abstract

Our aim in this paper is to make a novel interpretation of the relation between the statistical deferred Cesaro summability method and statistical convergence based on a certain subsequence for sequences of real or complex numbers. In line with this aim, we introduce a necessary and sufficient Tauberian condition of Moricz-type for statistically deferred Cesaro summable sequences. In addition, we define the concepts of statistical deferred slow decrease and statistical deferred slow oscillation for a sequence of real and complex numbers, respectively. As a result, we derive some Tauberian conditions controlling O-L- and O-oscillatory behavior of a sequence in the statistical sense.