?-Statistical Convergence of Order ? (vol 31, pg 953, 2011)

Abstract

The sequences defined in Example 3 and Example 4 do not serve our purpose for any lambda = (lambda(n)). Because this sequences are just the sequences x = (x(k)) = (k) and x = (x(k)) = (1) respectively and any term of these sequences can not be 0. In this short not we give Example 3* and Example 4* to show that the inclusions given in Theorem 2.4 and Theorem 2.9 are strict for some lambda = (lambda(n)), alpha and beta such that 0 < alpha < beta <= 1.