f-Wijsman Lacunary statistical convergence of order α

This study is prepared as five chapter. In the first chapter which is organized as the entrance section has been given historical background of the subject. In the second chapter, we give the fundamental definitions and theorems. Additionally we give the concepts of natural density, statistical convergence and strong p-Cesaro summability. In the third chapter, we define lacunary statistical convergence of order α of sequences and strong p-lacunary convergence of order α of sequence and give some relations between of these concepts. In the fourth chapter, we define the concepts of statistical convergence and strong p-Cesaro summability for sequences of sets and give some relations between of these spaces. In the fifth chapter which is organized original part of this thesis has been generalized the concepts of lacunary statistical convergence of order α and strong p-lacunary convergence of order α of real sequences to the concepts of lacunary statistical convergence of order α and strong p-lacunary convergence of order α of sets sequences, where θ=(k_r ) is a lacunary sequence, The results which we obtained in this study are much more general than those obtained by others. Key Words: Statistical Convergence, Lacunary Sequence, Modulus Function, Cesaro Summabilitiy.