Abstract In this paper we introduce the notion of deferred arithmetic statistical convergence, which combines the arithmetic approach to convergence with a deferred statistical scheme. After presenting basic examples, we study fundamental structural properties of the resulting class of sequences. In particular, we establish linearity, investigate inclusion relations with arithmetic statistical convergence and deferred arithmetic convergence, and prove that deferred arithmetic convergence implies deferred arithmetic statistical convergence. Furthermore, we show that under a uniform boundedness condition on the arithmetic differences, the two notions coincide. Finally, we present continuity-type results for sequences of functions and discuss the stability of deferred arithmetic statistical continuity under uniform limits.
GÜL et al. (Thu,) studied this question.