turkmath.org

Summability of real valued sequences has been a subject of study for many mathematicians over the last century and in recent years. Many different types of convergence including statistical, Cesaro, almost and ideal convergence, and related properties have been researched. In some studies, the relationship of a sequence and its subsequences regarding some type of summability was investigated. For this purpose two different gauges of size were used: Lebesgue measure and Baire category, yielding many interesting results.  Here we will present some of our results of this kind, related to statistical, uniform statistical and Cesaro convergence.