Further remarks on uniform statistical convergence of order \(\alpha\). (English) Zbl 1517.40003
Following a summability method (called uniform statistical convergence by H. Albayrak and S. Pehlivan [Appl. Math. Lett. 23, No. 10, 1203–1207 (2010; Zbl 1206.40001)] corresponding to uniform density by V. Baláž and T. Šalát [Math. Commun. 11, No. 1, 1–7 (2006; Zbl 1114.40001)], the author introduces a new concept called \(I_u\) convergence of order \(\alpha\), the uniform statistical convergence of order \(\alpha\), \(0<\alpha\leq 1\), and obtains its basic properties. It is worth noting that the author states some open problems for interested readers.
Reviewer: İbrahim Çanak (İzmir)
MSC:
| 40A35 | Ideal and statistical convergence |
| 40A05 | Convergence and divergence of series and sequences |
| 00A27 | Lists of open problems |
Keywords:
uniform density of order \(\alpha\); \(I_u\)-convergence of order \(\alpha\); (uniform) strong \(p\)-Cesàro summability of order \(\alpha\); almost convergence of order \(\alpha\)References:
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