On $\Cal{I}$ and $\Cal{I}^*$-equal convergence and an Egoroff-type theorem

Authors

  • Pratulananda Das Department of Mathematics, Jadavpur University, Jadavpur, Kol-32, West Bengal, India Author
  • Sudipta Dutta Department of Mathematics, Jadavpur University, Jadavpur, Kol-32, West Bengal, India Author
  • Sudip Kumar Pal Department of Mathematics, Jadavpur University, Jadavpur, Kol-32, West Bengal, India Author

Keywords:

Ideal, filter, $\Cal{I}$ and $\Cal{I}^*$-equal convergence, $P$-ideal, Chain condition, $\Cal{I}^*$-uniform equal convergence, $\Cal{I}^*$-almost uniform equal convergence, $\Cal{I}^*$-quasi vanishing restriction, Egoroff Theorem

Subjects:

40G15, 40A99, 46A99

Abstract

In this paper we extend the notion of equal convergence ofCsászár and Laczkovich with the help of ideals of the set ofpositive integers and introduce the ideas of $\Cal{I}$ and$\Cal{I}^*$-equal convergence and prove certain properties.Throughout the investigation two classes of ideals, onesatisfying "Chain Condition'' and another called $P$-ideals playa very important role. We also introduce certain related notionsof convergence and prove an Egoroff-type theorem for$\Cal{I}^*$-equal convergence.

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Published

2014-04-15

Issue

Vol. 66 No. 2 (2014): Vol. 66, Issue 2

Section

Articles

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Copyright (c) 2014 Authors retain copyright to their work.

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This work is licensed under a Creative Commons Attribution 4.0 International License.