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On strongly regular dual summability methods. (English) Zbl 0587.40005
The author considers two methods of summability A and A’ the sequence and series method respectively and calls them dual methods. He defines strong regularity of the A’ method and establishes the following: A regular matrix $A'=(a'\!\sb{nk})$ is strongly regular if and only if it satisfies the conditions (i) $\lim\sb{k}a'\!\sb{nk}=0$, for each n, (ii) $\lim\sb{n}\sum\sp{\infty}\sb{k=0}\vert \Delta\sp 2a'\!\sb{nk}\vert =0$. He also establishes that given two dual methods A and A’, A is strongly regular if and only if A’ is strongly regular.
Reviewer: I.Sukla

40A99Convergence and divergence of infinite limiting processes