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Parameswaran, M. R.
- On the Translativity of Hausdorff and Some Related Methods of Summability
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1 Ramanujan Institute of Mathematics, Madras, IN
1 Ramanujan Institute of Mathematics, Madras, IN
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The Journal of the Indian Mathematical Society, Vol 23, No 1-2 (1959), Pagination: 45-64Abstract
The general problem of translativity for Hausdorff methods (H, μn) has been studied by Agnew [1] and recently by Kuttner [7] who has obtained (i) a set of necessary conditions, and (ii) a set of sufficient conditions, for translativity; Kuttner's conditions are all on the Hausdorff matrix and he makes no restrictions on the sequences involved.- Note on a Theorem of Mazur and Orlicz in Summability
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1 Ramanujan Institute of Mathematics, Madras, IN
1 Ramanujan Institute of Mathematics, Madras, IN
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The Journal of the Indian Mathematical Society, Vol 22, No 2 (1958), Pagination: 65-75Abstract
In this note we shall prove some extensions of certain theorems of Mazur and Orlicz [5] and some applications thereof. In these theorems a sequence x = {xn} is transformed into another sequence y = {yn}.- Two Tauberian Theorems for Functions Summable (A)
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1 Ramanujan Institute of Mathematics, Madras, IN
1 Ramanujan Institute of Mathematics, Madras, IN
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The Journal of the Indian Mathematical Society, Vol 22, No 2 (1958), Pagination: 77-83Abstract
Let s = s(u) be a function of bounded variation in every finite interval of u ≥ 0 and supposed, for simplicity, to be such that s(0) = 0.- On a Comparison between the Cesaro and Borel Methods of Summability
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1 Ramanujan Institute of Mathematics, Madras, IN
1 Ramanujan Institute of Mathematics, Madras, IN
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The Journal of the Indian Mathematical Society, Vol 22, No 2 (1958), Pagination: 85-92Abstract
It is well known that the Abel method of summability is strictly stronger than the Cesaro method Cr for every r, and that the Borel's (exponential) method is likewise strictly stronger than the Euler-Knopp method Eα for every α (0 < a ≤ 1).- On the Reciprocal of a K-Matrix*
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1 Ramanujan Institute of Mathematics, Madras, IN
1 Ramanujan Institute of Mathematics, Madras, IN
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The Journal of the Indian Mathematical Society, Vol 20, No 1-3 (1956), Pagination: 329-331Abstract
If the K-matrix A has a two-sided Kr-reciprocal A-1, then A-1 is itself a K-matrix.
For definitions and properties of K-and Kr-matrices, see Cooke [ 3 ] ; we follow the notation used in this book. The result is of interest, since the sets of Kr- and if-matrices are Banach algebras, the former containing the latter as a subalgebra.