Convergence of linking Baskakov-type operators

Abstract

In this paper we consider a link B n,ρ between Baskakov type operators B n,∞ and genuine Baskakov-Durrmeyer type operators B n,1 depending on a positive real parameter ρ. The topic of the present paper is the pointwise limit relation B n,ρ f (x) → B n,∞ f (x) as ρ → ∞ for x ≥ 0. As a main result we derive uniform convergence on each compact subinterval of the positive real axis for all continuous functions f of polynomial growth.