Statistical convergence of order α defined by Lucas numbers

In the first part of this study which consists of five parts, the concepts that form the basis for our subject are explained and some of the research that has been done in the literature about these concepts are mentioned and some of these studies have been referred to. In the second part, the basic definitions and theorems that form the basis of our work are mentioned. With the help of the concept of natural density, we explain the concepts of statistical convergence and statistical convergence of order α with some examples. In the third section in which we give our results, a new regular matrix and a new sequence space are created by using Lucas numbers. Using the Lucas sequences obtained by the help of the terms of this matrix, some properties related to statistical convergence and statistical convergence of order α are examined. In the fourth section, we evaluate the contribution of the findings to the literature and what can be done afterwards. In the last section, the articles, books and theses that we used during the completion of this study are cited.