The Journal of the Indian Mathematical Society

M. R. Parameswaran ¹

Affiliations
1 Ramanujan Institute of Mathematics, Madras, IN

Abstract

The general problem of translativity for Hausdorff methods (H, μ_n) 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.

Full Text

     

M. R. Parameswaran ¹

Affiliations
1 Ramanujan Institute of Mathematics, Madras, IN

Abstract

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 = {x_n} is transformed into another sequence y = {y_n}.

Full Text

     

M. R. Parameswaran ¹

Affiliations
1 Ramanujan Institute of Mathematics, Madras, IN

Abstract

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.

Full Text

     

M. R. Parameswaran ¹

Affiliations
1 Ramanujan Institute of Mathematics, Madras, IN

Abstract

It is well known that the Abel method of summability is strictly stronger than the Cesaro method C^r 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).

Full Text

     

M. R. Parameswaran ¹

Affiliations
1 Ramanujan Institute of Mathematics, Madras, IN

Abstract

If the K-matrix A has a two-sided K_r-reciprocal A^-1, then A^-1 is itself a K-matrix.

For definitions and properties of K-and K_r-matrices, see Cooke [ 3 ] ; we follow the notation used in this book. The result is of interest, since the sets of K_r- and if-matrices are Banach algebras, the former containing the latter as a subalgebra.

Full Text