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I and I * -convergence in topological spaces

Benoy Kumar Lahiri, Pratulananda Das (2005)

Mathematica Bohemica

We extend the idea of I -convergence and I * -convergence of sequences to a topological space and derive several basic properties of these concepts in the topological space.

I-convergence theorems for a class of k-positive linear operators

Mehmet Özarslan (2009)

Open Mathematics

In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.

Ideal version of Ramsey's theorem

Rafał Filipów, Nikodem Mrożek, Ireneusz Recław, Piotr Szuca (2011)

Czechoslovak Mathematical Journal

We consider various forms of Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem which are connected with ideals of subsets of natural numbers. We characterize ideals with properties considered. We show that, in a sense, Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem characterize the same class of ideals. We use our results to show some versions of density Ramsey's theorem (these are similar to generalizations shown in [P....

Iterated series and the Hellinger-Toeplitz theorem.

Charles Swartz (1992)

Publicacions Matemàtiques

We show that an iterated double series condition due to Antosik implies the uniform convergence of the double series. An application of Antosik's condition is given to the derivation of a vector form of the Hellinger-Toeplitz theorem.

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