Revision as of 11:29, 16 September 2016

S1319516613000340

In the above referenced paper, we obtained a new lacunary sequence ${\textstyle \theta ^{'}=(P_{k_{r}})}$ using a sequence of positive real numbers ${\textstyle (p_{k})}$. But we did not notice a lack of provision in the article. Throughout the paper, ${\textstyle H_{r}\rightarrow \infty }$ as ${\textstyle r\rightarrow \infty }$ should be assumed. The reason for adding such a provision is that the assumption “${\textstyle P_{n}\rightarrow \infty }$ as ${\textstyle n\rightarrow \infty }$” may not be enough to obtain the condition “${\textstyle H_{r}\rightarrow \infty }$ as ${\textstyle r\rightarrow \infty }$”.

Also, in the hypothesis of Theorem 6, the condition ${\textstyle I_{r}^{'}\subset I_{r}}$ should be added, whereas the condition ${\textstyle I_{r}\subset I_{r}^{'}}$ should be added in the hypothesis of Theorem 7 and Corollary 3.