A Novel Study on q-Fibonacci Sequence Spaces and Their Geometric Properties

In this study we develop a q-Fibonacci matrix F(q)=(fqₙᵥ)n,v∈ N₀ given by aligned fqₙᵥ=\ arrayccc qᵛ⁺¹fᵥ₊₁(q)fₙ₊₃(q)-1&, & 0≤ v≤ n, \\ 0 &, & v>n. array. aligned where ( fᵥ(q)) represents a sequence of q-Fibonacci numbers. By utilizing the matrix F(q) , we define matrix domains ₚ (F(q)):=( ₚ)F(q) (0<p< ∞ ) and _∞ (F(q)):=( _∞ )F(q) also known as q-Fibonacci sequence spaces. We obtain Schauder basis for the space ₚ (F(q)) and determine Alpha-( α -), Beta-( β -) and Gamma-( γ -) duals of the newly defined spaces. We obtain some results related to matrix transformations from the spaces ₚ(F(q)) and _∞ (F(q)) to classical sequence spaces _∞ , c and c₀ . We also examined some of the geometric properties like approximation property, Dunford–Pettis property, Hahn–Banach extension property, and rotundity of the spaces ₚ(F(q)) and _∞ (F(q)) .