Convergence types of order α for real sequences

This thesis study consists of six sections. The first section is dedicated to an introduction part by giving progress of the topic over the years. In the second section some elemental notions are mentioned in order to be more understandable of the work. In the third section, statistical convergence of order α and strong p-Cesàro summability concepts for real sequences are introduced, some properties and relationships between them are examined. In the forth section, lacunary statistical convergence of order α concept for real sequences is introduced, its properties and inclusion relations with statistical convergence of order α concept are given. Also, strong p-lacunary statistical convergence of order α notion is presented, the interactions among the two are explained with examples and theorems. In the fifth section, I-statistical and I-lacunary statistical convergence ideas for real sequences are defined, their some features are offered. Finally, in the sixth section, resources applied for this study are listed.