Some Tauberian theorems for statistical (C,1) summability

Schoenberg (1959) [23] proved that if a sequence (xk) is bounded and statistically convergent to L then it is statistically summable (C,1) to L. However the converse is not true. In this paper we prove necessary and sufficient Tauberian conditions based on generator sequences under which statistical convergence follows from statistical summability (C,1).