### Abstract

This paper is a study of summability methods that are based on Dirichlet convolution. If f(n) is a function on positive integers and x is a sequence such that lim_{n→∞} Σ_{k≤n} 1/k(f * x)(k) = L, then x is said to be A_{f}-summable to L. The necessary and sufficient condition for the matrix A_{f} to preserve bounded variation of sequences is established. Also, the matrix A_{f} is investigated as l - l and G - G mappings. The strength of the A_{f}-matrix is also discussed.

Original language | English (US) |
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Pages (from-to) | 498-508 |

Number of pages | 11 |

Journal | Canadian Mathematical Bulletin |

Volume | 40 |

Issue number | 4 |

State | Published - Dec 1997 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Canadian Mathematical Bulletin*,

*40*(4), 498-508.

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*Canadian Mathematical Bulletin*, vol. 40, no. 4, pp. 498-508.

**Matrix transformations based on Dirichlet convolution.** / Selvaraj, Chikkanna R.; Selvaraj, Suguna.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Matrix transformations based on Dirichlet convolution

AU - Selvaraj, Chikkanna R.

AU - Selvaraj, Suguna

PY - 1997/12

Y1 - 1997/12

N2 - This paper is a study of summability methods that are based on Dirichlet convolution. If f(n) is a function on positive integers and x is a sequence such that limn→∞ Σk≤n 1/k(f * x)(k) = L, then x is said to be Af-summable to L. The necessary and sufficient condition for the matrix Af to preserve bounded variation of sequences is established. Also, the matrix Af is investigated as l - l and G - G mappings. The strength of the Af-matrix is also discussed.

AB - This paper is a study of summability methods that are based on Dirichlet convolution. If f(n) is a function on positive integers and x is a sequence such that limn→∞ Σk≤n 1/k(f * x)(k) = L, then x is said to be Af-summable to L. The necessary and sufficient condition for the matrix Af to preserve bounded variation of sequences is established. Also, the matrix Af is investigated as l - l and G - G mappings. The strength of the Af-matrix is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=0031461120&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031461120&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031461120

VL - 40

SP - 498

EP - 508

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

SN - 0008-4395

IS - 4

ER -