Statistical convergence of difference sequences in connection with modulus functions and some generalizations

In this thesis by using difference sequences and modulus functions, we give some definitions and theorems about statistical convergence, statistical boundedness, strong Cesàro summability and statistical convergence of order and strong Cesàro summability of order with respect to modulus functions. In the beginning we give the relations between the sets of statistically convergent sequences and statistically bounded sequences and we give some relations between them. Then we provide the relations between the sets of statistically convergent sequences and statistically bounded sequences. After that we discuss the relations between and , and , and , and , and for different modulus functions and under certain conditions. Finally we give some relations between the sets of statistically convergent sequences of order and strongly Cesàro summable sequences of order . Kizmaz defined the difference sequence spaces and which are Banach spaces, where .