The investigation of statistical convergence types of order α. for double function sequences

This study consists of five chapters. In the first chapter, basic definitions, theorems and the date of the work are given. In the second chapter lacunary statistical convergence of the differences of the double function sequence in the second chapter, natural density, statistical convergence, Cesaro summability in sequences, α for difference sequences. pointwise statistical convergence, uniform and statistical convergence in real valued double function sequences, strong double Cesaro convergence, real valued double sequences. are explained with examples. Materials and methods used in the third chapter are given. In the fourth chapter, for double function sequence Δ𝑟- pointwise statistical convergence of order 𝛼̂, the definitions and theorems strong Δ𝑝- Cesaro summability of order 𝛼̃, (𝑉, 𝜆, 𝜇) summation of order 𝛼̃ are given and inclusion relations for α,β are examined. Generalized la vallee-pousin mean averages are given and the inclusion relations for separate forces such as 𝛼, 𝛽 are examined. Then the differences of the double indices of function sequence are given by lacunary statistical convergence definition and theorems. In the fifth chapter, conclusions and recommendations are given. In the conclusion section, the information on the thesis and the lacunary are suggested.