On f-lacunary stati̇sti̇cal boundedness of order α

This study is prepared as eight chapters with introduction and conclusion. 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 , lacunary statistical convergence, λ -statistical convergence, generalized De-la Vallée-Poussin mean and strong p-lacunarys summability. In the third chapter, we define lacunary density of order α. statistical convergence of order α, lacunary statistical Cauchy of order α of sequences and give some relations between of these concepts. In the fourth chapter, we define the concepts of statistical boundedness and give some relations between statistical convergence and statistical boundedness. In the fifth chapter, we define the concepts of lacunary statistical boundedness and give some relations between lacunary statistical convergence and lacunary statistical boundedness In the sixth chapter, we define the concepts of lacunary statistical boundedness of order α and give some relations between statistical boundedness of order α and lacunary statistical boundedness of order α. In the fifth chapter which is organized original part of this thesis has been generalized the concept of lacunary statistical boundedness to the concepts of f-lacunary statistical boundedness of order α, where θ=(k_r ) is a lacunary sequence, and f is an unbounded modulus function. Finally we give a conclusion. Key Words: Statistical Convergence, Lacunary Sequence, Modulus Function, Cesaro Summabilitiy.