Statistical Deferred Cesàro Summability and Its Applications to Tauberian Theory

Our aim in this paper is to make a novel interpretation of the relation between the statistical deferred Cesàro 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 Móricz-type for statistically deferred Cesàro 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 - and O_L-oscillatory behavior of a sequence in the statistical sense.