On some type of convergence of order /alpha-

This thesis consists of five chapters. In the first chapter, the concept of statistical convergence of order alpha is mentioned briefly. In the second chapter, the literature on the subject was examined. In the third chapter, the fundamental definitions and notations are given. The fourth chapter, which is the original part of this thesis, consists of two sections. In the first section of fourth chapter, the concept of weighted lacunary almost statistical convergence of order alpha of double sequences was defined and some inclusion relations were given. In the second section of the fourth chapter, the ideal version of weighted lacunary statistical convergence of sequences of order alpha was examined. Further, some inclusion relations were given. In the last chapter, we evaluate the results obtained.