In this study we investigate the convergence theorems such as bounded convergence theorem, Fatou's lemma, monotone convergence theorem and dominated convergence theorem for measurable functions depending upon the concept of statistical convergence.

In this work, we determined the general terms of all almost balancing numbers of first and second type in terms of balancing numbers and conversely we determined the general terms of all balancing numbers in terms of all almost balancing numbers of first and second type. We also set a correspondence between all almost balancing numbers of first and second type and Pell numbers.

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In this work, we determine the general terms of t-cobalancers, t-cobalancing numbers and Lucas t-cobalancing numbers by solving the Pell equation 2x 2 − y 2 = 2t 2 − 1 for some fixed integer t ≥ 1.