Lacunary statistical convergence of order alpha and I-convergence of order alpha

Lacunary Statistical Convergence of Order ? and I-Convergence of Order ? This study is prepared as five chapter.In the first chapter, we give historical background of the subject.In the second chapter, we give the fundamental definitions and theorems. In the third chapter, we examine statistical convergence of order ? and their associate concepts. In the first section of fourth chapter, we define lacunary statistical convergence of order ? of sequence space S_?^? and strong p-lacunary convergence of order ? of sequence space N_?^? (p) using lacunary sequence ?=(k_r ) and give some inclusion relations between of these spaces. In the second section of this chapter, we define strongly N_?^? (M,(p))- summable of sequence space with respect to the Orlicz function M and give some relations that belong to these classes. In the last section, we define sequence space w_((p))^? [?,f] with respect to the modulus function f and give some relations that belong to these spaces. In the fifth chapter, we define I-convergence of order ? of sequence space S^? (I), (?,I)-convergence of order ? of sequence space S_?^? (I) and examine some properties these spaces. Key Words: Statistical Convergence, Lacunary Sequence, Orlicz Function Modulus Function, Ideal.