New Integrated and Differentiated Sequence Spaces ∫ b_p^(r,s) and db_p^(r,s)

Abstract

In this work, we construct new sequence spaces by combining the integrated and differentiated sequence spaces with the binomial matrix. Firstly, we provide information about basic matters such as sequence spaces and matrix domain. Subsequently we briefly summarize some sequence spaces generated by the binomial matrix. Thereafter, we define the integrated and differentiated sequence spaces and establish the new sequence spaces. Afterwards, we examine some properties and the inclusion relations of these new sequence spaces. We also determine the α, β and γ-duals of the integrated and differentiated sequence spaces. Finally, we characterize some matrix classes associated with the new sequence spaces.