I-Statistical Rough Convergence of Order α

Abstract

The aim of this paper is to define the concept of I-statistical (I-st) rough convergence of order α (0 < α ≤ 1). It proposes the concept of I-st bounded of order α. Moreover, the necessary and sufficient condition for a sequence (xk) to be I-st bounded of order α is studied. In addition, the necessary and sufficient condition for a sequence (xk) to be I-st convergent of order α is examined. Finally, the need for further research studies are discussed.