On statistical A-summability

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