On Generalized Product of Ces´aro Summable Series
Abstract
Summability is more general than that of ordinary convergence. This is a
branch of mathematical analysis in which an infinite series which is usually divergent
can converge to a finite sum s (say) by ordinary summation techniques
and become summable with the help of different summation means or methods.
Many authors have discussed various summability methods. C method was
given by Ernesto Ces´aro such that ordinary Ces´aro summation was written as
(C, 1) summation whereas generalised Ces´aro summation was given as (C, α). In
1913, Hardy [5] proved a Theorem on (C, α), α > 0 summability of the series.
(C, α), [C, α], |C, α| denotes respectively ordinary, strong and absolute Ces´aro
summability methods. The product of ordinary and absolute summability has
been discussed by Borwein [1]. In this paper generalized product of ordinary and
absolute summability has been defined and some of its properties investigated.