In the current chapter, we introduce some special methods of summability, viz. the Abel method, the Weighted Mean method, the Euler method and the \((M, \lambda _n)\) or Natarajan method, and study their properties extensively. The connection between the Abel method and the Natarajan method is brought out.
The Weighted Mean method Hardy Móricz and Rhoades The \((M, \lambda _n)\) or Natarajan method Y-method Consistent Translative Inclusion theorem Equivalence theorem The Abel method Product theorem The Euler method Invertible
This is a preview of subscription content, log in to check access
Peyerimhoff, A.: Lectures on Summability. Lecture Notes in Mathematics, vol. 107. Springer, Berlin (1969)MATHGoogle Scholar
Natarajan, P.N.: A generalization of a theorem of Móricz and Rhoades on Weighted means. Comment. Math. Prace Mat. 52, 29–37 (2012)MATHGoogle Scholar
Hardy, G.H.: A theorem concerning summable series. Proc. Cambridge Philos. Soc. 20, 304–307 (1920-21)Google Scholar
Móricz, F., Rhoades, B.E.: An equivalent reformulation of summability by weighted mean methods. revisited. Linear Algebra Appl. 349, 187–192 (2002)MathSciNetCrossRefMATHGoogle Scholar