On asymptotically Lacunary i-equivalent sequences defined by a modulus function

This thesis consists of five main chapters. In the second chapter, the basic concepts and definitions that are present in the literatüre and necessary for a better understanding of the thesis are mentioned. In the third chapter, the definitions of basic concepts related to asymptotic lacunary ideal equivalence defined by the modulus function of real number sequences are given and theorems and their proofs are examined. In the fourth chapter, by using a positive p=p_k sequence, the definitions of basic concepts related to the asymptotic lacunary ideal equivalence defined by the modulus function of the real number sequences are given and the theorems and proofs which examine some coverage and necessity relationships between these concepts are examined. In the fifth section, which is the last chapter, the sources in the literatüre that we use during our study are listed.