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Summability and Convergence Using Ideals

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Current Topics in Summability Theory and Applications

Abstract

In this chapter, we concentrate on different concepts of summability and convergence using the notions of ideals and essentially present the basic developments of these notions. Starting with the first notion of ideal convergence we go on to discuss in detail how the notion has been extended over the years from single sequences to double sequences and nets and discuss some of the most recent advances made in this area, in particular applications of ideal convergence to the theory of convergence of sequences of functions. We also list many problems which still remain open.

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, 700032, West Bengal, India

    Pratulananda Das

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  1. Pratulananda Das
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Editors and Affiliations

  1. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  2. Department of Mathematics, Indiana University, Bloomington, Indiana, USA

    Billy E. Rhoades

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Pratulananda Das (2016). Summability and Convergence Using Ideals. In: Dutta, H., E. Rhoades, B. (eds) Current Topics in Summability Theory and Applications. Springer, Singapore. https://doi.org/10.1007/978-981-10-0913-6_3

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