On Lacunary invariant statistical convergence

This thesis consists of six chapters. In the first chapter, historical development of related notions of the thesis subject was mentioned. In the second chapter, some ba- sic definitions, concepts, examples and theorems related to study were given. In the third chapter, giving definitions, concepts, and theorems related to lacunary strong invariant convergence, invariant statistical convergence and lacunary invariant sta- tistical convergence and some inclusion relations were given. In the fourth chapter, concepts of invariant statistical convergence and A-invariant statistical convergence and inclusion relations between this concepts were given. Also, matrix transforma- tions were investigated. In the fifth chapter, giving concepts of lacunary statistical invariant summability and strong lacunary q-invariant convergence relations between this concepts were investigated. In the sixth chapter, the sources in the literature that we use during our study are given.