Lacunary weak statistical convergence

In this thesis, we give the concepts of statistical convergence of order α for 0<α≤1, strong p-Cesàro summability of order α for 0<α≤1 and weak statistical convergence. Also, some relations between statistical convergence of order α and strong p-Cesàro summability of order α are given for 0<α≤1. Furthermore, we provide lacunary weak statistical convergence of order α and weak N_θ^α-Summability of order for 0<α≤1. In the last section, we introduce the ∆-lacunary weak statistical convergence of order α and weak N_θ^α (∆)-Summability of order α for 0<α≤1. We also give some inclusion relations between these concepts.