We improve and generalize a result on a local property of |T |k summability of factored Fourier series due to Sarıgöl [6].

In this paper, a general theorem concerning absolute matrix summability is established by applying the concepts of almost increasing and δ-quasi-monotone sequences.

In this paper, we prove a known theorem dealing with φ− | C, α, β |k summability factors under more weaker conditions. This theorem also includes several new results.

Abstract The main object of this article is to introduce the concepts ( f, ρ )− statistical convergence order α and strong summability sequences real numbers give some inclusion relations between these spaces.

In this paper,  we determine necessary and sufficient Tauberian conditions under which convergence in Pringsheim's sense of a double sequence of fuzzy numbers follows from its $(C,1,1)$ summability. These conditions are satisfied if the double sequence of fuzzy numbers is slowly oscillating in different senses. We also construct some interesting double sequences of fuzzy numbers.