Asymptotic lacunary ideal invariant equivalent sequences

This study consists of six chapters. In the first chapter, the historical development of the thesis subject and general literature information are given. In the second chapter, some basic definitions and notations that are necessary for the study to be more understandable are mentioned. In the third chapter, some concepts of asymptotic lacunary equivalence for single real number sequences are introduced and the relationships between these concepts are given. Also, the relationship between these concepts and the concept of asymptotic lacunary invariant statistical equivalence are examined. In the fourth chapter, some concepts of asymptotic lacunary equivalence in Wijsman sense for single set sequences are presented and the relationships between these concepts are given. Also, the relationship between these concepts with Wijsman asymptotic lacunary invariant equivalence and Wijsman asymptotic lacunary invariant statistical equivalence is mentioned. In the fifth chapter, some concepts of asymptotic lacunary equivalence for double set sequences are introduced and the relationships between these concepts are studied. In the last chapter, the references that used in this study are listed.