On Some Analytical Relations Between Double Summability Methods of Abel-Natarajan

Josef Al Jumayel

Faculty Of Science, Beirut Arab University, Beirut, Lebanon

Abstract

This paper is dedicated to study the analytical relations between Abel's double summability method and Natarajan's double summability method, where many theorems that draw a bridge between the mentioned methods will be obtained. The main result of our work is to prove that that summability by Natarajan's method implies summability by Abel's method in one or two variables. On the other hand, we illustrate some related examples to clarify the validity of our approach.

Keywords: Natarajan's method; Abel's method; summability.