On statistical A-summability
Let A = (a(nk))(infinity)(n,k=1) be an infinite matrix and x = (x(k))(infinity)(k=1) a sequence of real or complex numbers. Then the A-transform of x is a sequence Ax = (A(n) (x)) where A(n)(x) = Sigma(infinity)(k=1)a(nk)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. (c) 2008 Elsevier Ltd. All rights reserved.
statistical a-summability a-summability statistical convergence core theorems