Comparison of Summability j(D; k)(C; ; )j p and Cesaro jC; jp Summability

Abstract

Summability is a branch of mathematical analysis in which an innite series
which is usually divergent can converge to a finite sum s (say) by ordinary summation
techniques and become summable with the help of deferent summation
means or 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; ). In 1913, Hardy [1] proved a theorem on (C; a),
a > 0 summability of the series.