ABSTRACT
This chapter focuses on the absolute summability which is an expansion of the concept of convergence and is a generalization of the concept of absolute convergence. It considers absolute summability and investigates some properties of absolute summability methods. The chapter discusses absolute summability regarding inclusion theorems and summability factors theorems. It deals with the general absolute inclusion theorem involving a pair of triangles and, as corollaries, inclusion theorems for special classes of triangles. A special type of summability of series and sequences, which differs from ordinary summability in that additional restrictions are imposed. For matrix summability methods the requirement is that the series and sequences obtained as a result of the transformation corresponding to the given summability method must be absolutely convergent. A summability method is to preserve absolute convergence of a series if it absolutely sums each absolutely convergent series.
