On statistical convergence of double sequences

This thesis consists of three chapters. The first chapter is devoted to the introduction. The second chapter includes definitions of necessary concepts and some theorems. Density of a set, convergence in single sequences, statistical convergence concepts are defined and their main properties are given. In the first part of the third chapter, convergence concepts in double sequences are introduced, their properties studied and examples about those are given. In the second part, basic information about double series are discussed. Moreover, convergence of double series and their absolute converge are defined. Examples related with those are solved. In the first part of the fourth chapter, in the light of second chapter, statistical convergence on double sequences is defined and it is studied with examples. Also, the relations between Pringsheim convergence and statistical convergence of double sequences are examined. Finally, in the second part, the connection between statistical convergence and strong Cesàro convergence of double sequences.