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Two theorems in the theory of summation of numerical series by lower triangular positive monotone matrices

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Abstract

For so-called monotone matrices, we establish necessary and sufficient conditions for the summation with them of some divergent sequences of 0 and 1 up to zero or some unbounded sequences of nonnegative numbers.

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References

  1. R. Cooke,Infinite Matrices and Sequence Spaces [Russian translation], Fizmatgiz, Moscow (1960).

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  2. G. Hardy,Divergent Series [Russian translation], Inostrannaya Literatura, Moscow (1951).

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Authors
  1. N. A. Davydov
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Additional information

Deceased.

National Pedagogic University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 553–555, April, 1999.

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Davydov, N.A. Two theorems in the theory of summation of numerical series by lower triangular positive monotone matrices. Ukr Math J 51, 618–621 (1999). https://doi.org/10.1007/BF02591763

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  • DOI: https://doi.org/10.1007/BF02591763

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