Absolute convergence fields of some triangular matrix methods

Kumar, Arun; Sahu, D. P.

doi:10.2140/pjm.1981.97.443

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Inclusion and Equivalence Relations1

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2018

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“…On inclusion and equivalence relations of different summability methods much work have been done already, see [1], [2], [3], [4], [5] and [7].…”

Section: Inclusion and Equivalence Relationsmentioning

confidence: 99%

Inclusion and equivalence relations between absolute Norlund and absolute weighted mean summability methods

Zraiqat

2018

B Soc Paran Mat

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In this paper, a set of conditions under which the absolute Nörlund summability method include in the absolute weighted mean method have been established. Three non-trivial examples to show that this inclusion holds have been given, and other three examples to show that even if both (N, r) and (N , q) are regular, the inclusion fails to holds have been constructed. The paper give two non-trivial examples to show that the equivalence of these two methods may holds. Finally, we give two examples to show that inclusion may holds in only one way without the other.Key Words: Inclusion and Equivalence Relation, Absolute Nörlund Summability Method. Let A be a sequence-to sequence transformationThe sequence {S n } is said to be summable (A) to s if t n −→ s as n −→ ∞, and if in addition {t n }, is of bounded variation, then {S n } is said to be absolutely summable (A) or summable |A|.

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“…On inclusion and equivalence relations of different summability methods much work have been done already, see [1], [2], [3], [4], [5] and [7].…”

Section: Inclusion and Equivalence Relationsmentioning

confidence: 99%