Generalized Euler‐Knopp method and convergence acceleration

Abstract

New propositions on λ‐boundedness for generalized Euler‐Knopp method of summability (ϵ, T), where ? is a linear bounded operator from Banach space X into X, are proved. Using these results are verified a proposition on convergence acceleration by (ϵ, T) and a Tauberian remainder theorem for (ϵ,T).

Key words:

• convergence acceleration
• summability methods
• Tauberian remainder theorems