Ibragimov, Zarif O.; Salimova, Diyora F. On an inequality in \(l_p(\mathbb C)\) involving Basel problem. (English) Zbl 1337.26043 Elem. Math. 70, No. 2, 79-81 (2015). The authors study the following conjecture: For all \(a=(a_{1}, a_{2}, \ldots )\in l_{2}(\mathbb C)\), the inequality \[ \sum_{n\geq 1}|a_{n}|^{2} \geq \frac{6}{\pi^{2}}\sum_{k\geq0}\left|\sum_{l\geq 0}\frac{1}{l+1}a_{2^{k}.(2l+1)}\right|^{2} \] posed by Z. Retkes [http://www.openproblemgarden.org/category/analysis] holds, and they give a very simple proof. In addition, an extension of the above conjecture to \(l_{p}(\mathbb C)\), \(p>1\) is also given. Reviewer: James Adedayo Oguntuase (Abeokuta) MSC: 26D15 Inequalities for sums, series and integrals 26D20 Other analytical inequalities Keywords:Cauchy-Schwarz inequality; Basel problem PDFBibTeX XMLCite \textit{Z. O. Ibragimov} and \textit{D. F. Salimova}, Elem. Math. 70, No. 2, 79--81 (2015; Zbl 1337.26043) Full Text: DOI Link