Sequence spaces derived by qλ operators in ₚ spaces and their geometric properties

In this paper, we establish a novel category of sequence spaces ₚ^qλ ℓ p q λ and ∞^qλ ℓ ∞ q λ by utlizing q -analogue Λq 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 ₚ ℓ p and ∞ ℓ ∞ . Moreover, we obtain the α -, β -, and γ -duals of these sequence spaces. We further characterize the class ( ₚ^qλ,X) ( ℓ p q λ , X ) of matrices, where X is any of the spaces ∞ ℓ ∞ , c , or c₀ c 0 . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space ₚ^qλ ℓ p q λ .