A new class of matrices and its applications to absolute summability factor theorems

We introduce a new class of matrices S(αn,ϕn)S(αn,ϕn) and establish a general absolute summability factor theorem by applying a recently defined absolute summability, |A,αn|k|A,αn|k summability, and the class S(αn,ϕn)S(αn,ϕn). As applications of the main result, we further verify that many well-known classes of matrices such as Cesàro’s matrices, Rhaly’s generalized Cesàro matrices, the pp-Cesàro matrices, and Riesz matrices are all in S(αn,ϕn)S(αn,ϕn) for some certain sequences {αn}{αn} and {ϕn}{ϕn}, and, therefore, many new factor theorems can be obtained under suitable conditions.