2020-01-01

In this thesis, we examine and study f-statistical convergence, f-statistical boundedness, f-strong Cesàro summability, strong f-lacunary summability and some other notions related to these concepts for sequences of real and complex numbers, where f is a modulus function. First, we give f-statistically convergent and f-statistically bounded sequences, and we provide the relations between these concepts. Then, we study f-strong Cesàro summability of sequences of real and complex numbers. Next, we establish the relations between the sets w^f and w^g, w^f and S^g, for different modulus functions f and g under some conditions, which is the original part of this thesis. Furthermore, for some special modulus functions, we obtain the relations between the sets w^f and w, S^f and S. After that, we study the concepts of f-statistical convergence of order α such that 0<α≤1 and f-strong Cesàro summability of order α such that 0<α≤1, and we also give the relations between these concepts. Finally, we give and study strong f-lacunary summability of order α, and we establish the relations between the sets N_θ^β (f) and N_θ^α (g), N_θ^α (f) and N_θ^β (g), N_θ^α (f) and S_θ^β (g), l_∞∩S_θ^α (f) and N_(θ^')^β (g), where f and g are different modulus functions under some conditions and α,β∈(0┤,├ 1] such that α≤β, which is another original part of this thesis. Furthermore, for some special modulus functions, we obtain the relations between the sets N_θ (f) and N_θ, N_θ^α (f) and N_θ^α for α∈(0┤,├ 1].