Doubly Iterated Matrix Methods of Summability

Absolute matrix summability methods

On absolute matrix summability methods

On Absolute Matrix Summability Methods

We have proved a theorem on |T, p n | k summability methods. This theorem includes a known theorem.

Matrix Summability in 7"-fields

when un = 22"-o a-inUi for all ra^O. If the sequence to sequence transformation associated with A is such that [u/[ ] exists and converges whenever [un] converges we call A a K matrix. If [uJ ] exists and converges to limn,,, un whenever this limit exists we call A a T matrix. Similar names for the series to sequence and the series to series matrices are TCi, 7\ and K2, T2 matrices respectively...

Iterated Point-Line Configurations Grow Doubly-Exponentially

Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and Radoičić (2003) showed that the limiting set is dense in the plane. We give doubly exponential upper and lower bounds on the number of points at each stage. The proof employs a variant of the Szemerédi-Trotter Theorem ...