?(?im)-Statistical Convergence of Order ?

Abstract

In this study, using the generalized difference operator Delta(m)(i) and a sequence lambda = (lambda(n)) which is a non-decreasing sequence of positive numbers tending to 8 such that lambda(n+1) <= lambda(n) + 1, lambda(1) = 1, we introduce the concepts of lambda(Delta(m)(i))-statistical convergence of order alpha (alpha is an element of (0, 1]) and strong lambda(Delta(m)(i))-Cesaro summablility of order alpha(alpha > 0). We establish some connections between lambda(Delta(m)(i))-statistical convergence of order a and strong lambda(Delta(m)(i))-Cesaro summablility of order a. It is shown that if a sequence is strongly lambda(Delta(m)(i))-Cesaro summable of order alpha, then it is lambda(Delta(m)(i))-statistically convergent of order beta in case 0 < alpha <= beta <= 1.