Matrix transformations on some sequence spaces related to strong Cesàro summability and boundedness

摘要

The spaces a0r(Δ),acr(Δ) and a∞r(Δ) introduced by Aydın and Başar [C. Aydın, F. Başar, Some new difference sequence spaces, Appl. Math. Comput. 157 (3) (2004) 677–693] can be considered as the matrix domains of a triangle in the sets of all sequences that are summable to zero, summable, and bounded by the Cesàro method of order 1. Here we define the sets of sequences which are the matrix domains of that triangle in the sets of all sequences that are summable, summable to zero, or bounded by the strong Cesàro method of order 1 with index p⩾1. We determine the β-duals of the new spaces and characterize matrix transformations on them into the sets of bounded, convergent and null sequences.