Some Topological and Geometric Properties of Some New Spaces of λ-Convergent and Bounded Series

The main purpose of this study is to introduce the spaces csλ, cs0λ, and bsλ which are BK-spaces of nonabsolute type. We prove that these spaces are linearly isomorphic to the spaces cs, cs0, and bs, respectively, and derive some inclusion relations. Additionally, Schauder bases of the spaces csλ and cs0λ have been constructed and the α-, β-, and γ-duals of these spaces have been computed. Besides, we characterize some matrix classes from the spaces csλ, cs0λ, and bsλ to the spaces lp, c, and c0, where 1≤p≤∞. Finally, we examine some geometric properties of these spaces as Gurarǐ’s modulus of convexity, property m∞, property (M), property WORTH, nonstrict Opial property, and weak fixed point property.