On I-convergence of double sequences

The present thesis consists of five chapters, which investigate the ideal convergence of double sequences.In the first chapter, brief history of double sequences and ideal convergence are given.In the second chapter, some basic concepts and theorems and properties of ideal convergence which are used in later chapters are presented.The third, fourth and fifth chapters of this thesis involve the original results.In the third chapter, ideal convergence and ideal Cauchy of double sequences in Pringsheim sense are expressed. Also, ideal convergence and ideal Cauchy of double sequence in regular sense are given and relationship between these concepts are examined.In the fourth chapter, multiplier sequence spaces for bounded and ideal convergence of double sequence are discussed.In the fifth chapter, definitions and theorems about pointwise and uniformly ideal convergence for double sequences of functions are given.