Convergence of linking Baskakov-type operators

In this paper we consider a link $$B_{n,\rho }$$Bn,ρ between Baskakov type operators $$B_{n,\infty }$$Bn,∞ and genuine Baskakov–Durrmeyer type operators $$ B_{n,1}$$Bn,1 depending on a positive real parameter $$\rho $$ρ. The topic of the present paper is the pointwise limit relation $$\left( B_{n,\rho }f\right) \left( x\right) \rightarrow \left( B_{n,\infty }f\right) \left( x\right) $$Bn,ρfx→Bn,∞fx as $$\rho \rightarrow \infty $$ρ→∞ for $$x\ge 0.$$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.