COMPARISON OF SUMMABILITY AND CESÅRO |(C, α)|p SUMMABILITY


By

Suyash Narayan Mishra1 and Laxmi Rathour2

1Department of Applied Sciences, Institute of Engineering and Technology, Lucknow-226028, Uttar Pradesh, India

2Ward Number-16, Bhagatbandh, Anuppur-484224, Madhya Pradesh, India

Email:snmishra@ietlucknow.ac.in, laxmirathour817@gmail.com

(Received : February 05, 2021 ; Informat : May 08,2021 ; Revised : February 12, 2022; Accepted : April 30,2022)


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 dierent summation means or methods. C method was given by Ernesto Cesåro such that ordinary Cesåro summation was written as ( C, l) summation whereas generalised Cesåro summation was given as (C, α). In 1913, Hardy [3] proved a theorem on (C, a), a > 0 summability of the series. In this paper, comparison of relative strength of absolute summabilities for functions has been investigated on different sets of parameters.


2020 Mathematical Sciences Classification: 42B05,42B08.

Keywords and Phrases: (D, k) means, (C, α) means, (C, α, b) means, (D, k)(C, α) product means, Fourier Series, Conjugate Series, Lebesgue Integral.



[Download full paper]