A Simple Sufficient Condition That a Method of Summability Be Stronger than Convergence
نویسندگان
چکیده
and a method A of summability by means of which a given sequence Su S2, • • • is summable to <r as w—»oo. If a sequence sn is summable A, we say that A {sn} exists and that sn belongs to the summability field of A. If sn is summable A to <r, we say that A {sn} = <r. The method A is regular if A {sn} = lim sn whenever lim sn exists. Toeplitz [l91l] (reference in bibliography at end of this paper) proved that A is regular if and only if the three conditions
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