Generalized lacunary statistical convergence and lacunary statistical boundedness

This study consists of the five main chapters. In the chapter 1 and 2, we give some informations about the historical development of studies which are related to thesis topic, and some fundamental definitions and theorems which are necessary in this study. In the third chapter, we define the concept of ∆f−lacunary statistical convergence of order β with respect to modulusfand sequence classes Sf,βθ(∆F), Wf,βθ[∆F,p], Wf,βθ(∆F,p) and Wβθ,f(∆F,p) and examine someproperties of them, where f is unbounded modulus, θis a lacunary sequence,(Xk)is a sequence offuzzy number, ∆ is difference operator and β∈(0,1]. In the fourth chapter, we define the concept of ∆f−lacunary statistical boundedness of order β with respect to modulus f and sequence class Sf,βθ(∆F,b) and give some inclusion relations between the other sequence classes existing in the literature. Also, we examine the topological properties like symmetricity, monotony, etc. In the fifth and last chapter, we give the results obtained from the thesis.