Matrix transformation and statistical convergence

In this paper we will say that a sequence xk is λ, A-statistically convergent, if for every ε > 0,limn→∞1λn|{k∈In:|[AX]k-L|⩾ε}|=0with In = [n − λn + 1,n], where A is an infinite matrix and λ a strictly increasing sequence of positive numbers tending to infinity such that λ1 = 1 and λn+1 ⩽ λn + 1 for all n. Using the Banach algebra (w0(λ), w0(λ)) we get sufficient conditions to have a sequence λ, A−1- statistically convergent. Then we deduce conditions for a sequence to be λ  , N¯q- statistically convergent. Finally we get results in the cases when A is the operator C(μ) and the Cesàro operator.