(????? ????)????-Statistical Boundedness and Convergence of Order ????

Abstract

In this paper, we defined the concepts of (????? ????)????-statistical convergence and (????? ????)????-statistical boundedness for sequences ???? and ???? with nonzero terms. Then, we extend these concepts to the concepts of ?????,???? ???? ????-statistical convergence and ?????,???? ???? ????-statistical boundedness using the sequences (????????) satisfying the conditions ????1 = 1, ????????+1 ? ???????? + 1 and ???????? ? ? (???? ? ?). Then, using the concepts of ?????,???? ???? ????-statistical convergence and ?????,???? ???? ????- statistical boundedness, we defined the sequence spaces ?????,???? ???? ????(???????? ????) and ?????,???? ???? ????(???????? ????) with the help of numbers ???? satisfying the condition 0 < ???? ? 1. We also investigated the inclusion relations between these sequence spaces and between the sequence spaces obtained in some special cases.