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In the above referenced paper, we obtained a new lacunary sequence <math display="inline">\theta ^{{'}}=(P_{k_r})</math> using a sequence of positive real numbers <math display="inline">(p_k)</math>. But we did not notice a lack of provision in the article. Throughout the paper, <math display="inline">H_r\rightarrow \infty </math> as <math display="inline">r\rightarrow \infty </math> should be assumed. The reason for adding such a provision is that the assumption “<math display="inline">P_n\rightarrow \infty </math> as <math display="inline">n\rightarrow \infty </math>” may not be enough to obtain the condition “<math display="inline">H_r\rightarrow \infty </math> as <math display="inline">r\rightarrow \infty </math>”. | In the above referenced paper, we obtained a new lacunary sequence <math display="inline">\theta ^{{'}}=(P_{k_r})</math> using a sequence of positive real numbers <math display="inline">(p_k)</math>. But we did not notice a lack of provision in the article. Throughout the paper, <math display="inline">H_r\rightarrow \infty </math> as <math display="inline">r\rightarrow \infty </math> should be assumed. The reason for adding such a provision is that the assumption “<math display="inline">P_n\rightarrow \infty </math> as <math display="inline">n\rightarrow \infty </math>” may not be enough to obtain the condition “<math display="inline">H_r\rightarrow \infty </math> as <math display="inline">r\rightarrow \infty </math>”. | ||
Also, in the hypothesis of Theorem 6, the condition <math display="inline">I_r^{{'}}\subset I_r</math> should be added, whereas the condition <math display="inline">I_r\subset I_r^{{'}}</math> should be added in the hypothesis of Theorem 7 and Corollary 3. | Also, in the hypothesis of Theorem 6, the condition <math display="inline">I_r^{{'}}\subset I_r</math> should be added, whereas the condition <math display="inline">I_r\subset I_r^{{'}}</math> should be added in the hypothesis of Theorem 7 and Corollary 3. | ||
Latest revision as of 14:39, 7 October 2016
In the above referenced paper, we obtained a new lacunary sequence Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle \theta ^{{'}}=(P_{k_r})}
using a sequence of positive real numbers Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle (p_k)}
. But we did not notice a lack of provision in the article. Throughout the paper, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle H_r\rightarrow \infty }
as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle r\rightarrow \infty }
should be assumed. The reason for adding such a provision is that the assumption “Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle P_n\rightarrow \infty }
as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle n\rightarrow \infty }
” may not be enough to obtain the condition “Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle H_r\rightarrow \infty }
as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle r\rightarrow \infty }
”.
Also, in the hypothesis of Theorem 6, the condition Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle I_r^{{'}}\subset I_r}
should be added, whereas the condition Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://test.scipedia.com:8081/localhost/v1/":): {\textstyle I_r\subset I_r^{{'}}}
should be added in the hypothesis of Theorem 7 and Corollary 3.
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Published on 07/10/16
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