On statistical and I-convergence of double sequences of functions in 2-normed spaces

This thesis study consists of seven chapters. In the first chapter, the historical development of the subject discussed in the study is mentioned. In the second chapter, some basic notions necessary for a better understanding of the study are given. In the third chapter, introducing the concepts of pointwise and uniformly statistical convergence for double sequences of functions in 2-normed spaces, the theorems that give the relations between these concepts are proved. In the fourth chapter, statistical Cauchy sequence concept for double sequences of functions in 2-normed spaces is introduced and the theorems involving the relationships with statistical convergence are explained. In the fifth chapter, introducing the concept of I_2-convergence for double sequences of functions in 2-normed spaces, the theorems that give the properties of this concept are examined. In the sixth chapter, introducing the concept of I_2-Cauchy sequence for double sequences functions in 2-normed spaces, and some theorems that give the properties of this concept are explained. In the seventh chapter, the sources in the literature used during the study are listed.