On statistical A-summability

Let A = ( a n k ) n , k = 1 ∞ be an infinite matrix and x = ( x k ) k = 1 ∞ a sequence of real or complex numbers. Then the A -transform of x is a sequence A x = ( A n ( x ) ) where A n ( x ) = ∑ k = 1 ∞ a n k x k provided that the series converges for each n ; and the sequence x is said to be A -summable if A x is convergent. In this paper we define statistical A -summability of x , that is, x is said to be statistically A -summable if A x is statistically convergent. We study here many other related concepts and provide some interesting examples.