A generalization of Cesàro sequence spaces in the Orlicz space

In this paper, we generalize the Cesàro sequence spaces in the classic Banach space L_p to the generalized Orlicz space L_φ. We construct the space by replacing the norm ${\parallel \cdot \parallel }_p$ in L_p with modular ρ_φ in L_φ. This generalization has lead to the use of the Luxemburg norm to discuss some topological properties of the spaces. We prove results regarding to modular and norm convergence. We also describe some properties of the spaces and a closed subspaces of the space. (paper)