The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = (λn). Because this sequences are just the sequences x = (xk) = (k) and x = (xk) = (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 λ = (λn) , α and β such that 0 < α < β≤ 1.
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