New Sequence Spaces Derived by the Composition of Binomial and Quadruple Band Matrices

In this work, we construct the sequence spaces b_0^(a,b) (Q), b_c^(a,b) (Q) and b_∞^(a,b) (Q), derived from the combination of binomial and quadruple band matrices, where Q is a quadruple band matrix. The study is divided into four main sections. The first section provides some fundamental definitions and equations that will be used later. In the second section, detailed discussions are made on some works previously completed by various authors using the domain of the binomial matrix. Then, the three new sequence spaces b_0^(a,b) (Q), b_c^(a,b) (Q) and b_∞^(a,b) (Q) are defined. It is then shown that these obtained sequence spaces are BK-spaces. Following this, it is demonstrated that b_0^(a,b) (Q), b_c^(a,b) (Q) and b_∞^(a,b) (Q) sequence spaces are linearly isomorphic to the spaces c_0, c and l_∞, in turn, followed by some inclusion relations. In the third section, the Schauder bases of the new sequence spaces b_0^(a,b) (Q) and b_c^(a,b) (Q) are provided, and the α-, β- and γ- duals of b_0^(a,b) (Q), b_c^(a,b) (Q) and b_∞^(a,b) (Q) sequence spaces are determined. The fourth section characterizes some matrix classes. As a result, it is observed that the new matrix obtained from the combination of binomial and quadruple band matrices provides more general and comprehensive results than those obtained previously.