Some new insights into ideal convergence and subsequences

Abstract

Some results on the sets of almost convergent, statistically convergent, uniformly statistically convergent, I-convergent subsequences of (sn) have been obtained by many authors via establishing a one-to-one correspondence between the interval (0, 1] and the collection of all subsequences of a given sequence s = (sn). However, there are still some gaps in the existing literature. In this paper we plan to fill some of the gaps with new results. Some of them are easily derived from earlier results but they offer some new deeper insights.