Summability and Convergence Using Ideals

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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