Arithmetical summability and arithmetical convergence

This thesis consists of five main chapters. In the first part, the literature information that summarizes the importance of the subject in the thesis in the field of mathematics and the studies on the subject is presented. In the second part, some basic definitions and concepts that are well known in the mathematics literature and used in the thesis are noted. In the third chapter, basic concepts about arithmetic summable sequence space, arithmetic summable bounded sequence space and arithmetic convergent sequence space are given, and theorems examining the relationships between these concepts and their proofs are given. In the fourth chapter, a sequence space is introduced by using the concepts of arithmetic summability and multiplier sequence, and theorems and proofs that examine some important properties of this space are given. In the fifth chapter, which is the last chapter, the sources used during the thesis study and available in the literature are listed.