Conditions for the equivalence of power series and discrete power series methods of summability

Sefa Anı Sezer, İbrahim Çanak

Discrete power series methods were introduced and their regularity results were developed by Watson [Analysis (Munich), 18(1): 97--102, 1998]. It was shown by Watson that discrete power series method ($P_\lambda$) strictly includes corresponding power series method ($P$). In the present work we present theorems showing when ($P_\lambda$) and ($P$) are equivalent methods and when two discrete power series methods are equivalent.