Sequence spaces derived by q_λ operators in ℓ _p spaces and their geometric properties

In this paper, we establish a novel category of sequence spaces ℓ _p^q_λ and ℓ _∞^q_λ by utlizing q-analogue Λ^q of Λ-matrix. Our investigation outlines several topological characteristics and inclusion results of these newly introduced sequence spaces, specifically identifying them as BK-spaces. Subsequently, we demonstrate that these novel sequence spaces are of nonabsolute type and establish their isometric isomorphism with ℓ _p and ℓ _∞ . Moreover, we obtain the α-, β-, and γ-duals of these sequence spaces. We further characterize the class (ℓ _p^q_λ,X) of matrices, where X is any of the spaces ℓ _∞ , c, or c_0 . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space ℓ _p^q_λ .