Some asymptotic equivalence types

This thesis consists of six main parts. The first part is devoted to the introduction part that contains of the historical development of the subject and a general literature about it. In the second part, the basic concepts necessary for our work are given. In the third part, basic concepts related to the asymptotic lacunary statistical equivalence of real number sequences are introduced and the relations between them are shown with examples and theorems. In the fourth part, basic concepts related to the I-asymptotic lacunary statistical equivalence of real number sequences are given by using an I ideal; Their specific properties and the relations between these concepts are explained by examples and theorems. In the fifth part, the I-asymptotic lacunary statistical equivalence of real number sequences is generalized using the p=(p_k) sequence of positive real numbers. In the sixth section, which is the last chapter, the sources in the literature that we use during our study are listed.