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What stands out in this article is the sequence spaces of a new brand c λ 0 ( B) and c λ ( B), derived by using a double sequential band matrix B(r,s) which generalizes the previous work of Sönmez and Başar (Abstr. Appl. Anal. 2012Anal. :435076, 2012, where (r n )

Let λ denote any one of the classical spaces ∞ , c, c 0 and p of bounded, convergent, null and absolutely p-summable sequences, respectively, and λ also be the domain of the double sequential band matrix B( r, s) in the sequence space λ, where (r n ) ∞ n=0 and (s n ) ∞ n=0 are given convergent sequences of positive real numbers and 1 ≤ p < ∞. The present paper is devoted to studying the sequence space λ. Furthermore, the β-and γ -duals of the space λ are determined, the Schauder bases for the spaces c, c 0 and p

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