On order statistical and order i-convergence types

This thesis consists of five main chapters. In the first chapter, a general literature information about the importance and historical background of the thesis subject is given. In the second part, some basic concepts and definitions available in the literature and necessary for a better understanding of the thesis work are mentioned. In the third chapter, some features related to the metric are mentioned by remembering the γ metric in an L additive system. Keeping this in mind, the concept of order statistical convergence in the metric additive system (L,γ) is introduced and some related results are examined. In the fourth chapter, the concept of order ideal convergence in a (L,γ) metric additive system and some general properties related to this concept are discussed. In this sense, firstly, the concept of order ideal convergent is introduced and examples are given. Then, the concepts of order ideal constraint and OI^*-convergence were introduced and their relations with OI-convergence were examined. In the fifth section, which is the last chapter, the sources in the literatüre that we use during our study are listed.