Generalized Szász-Mirakjan type operators via q-calculus and approximation properties

摘要

The aim of this paper is to construct q-analogue of generalized Szász-Mirakjan type operators whose construction depend on a real valued function ρ. We prove that the new operators provide better weighted uniform approximation over [0, ∞). In terms of weighted moduli of smoothness, we obtain degrees of approximation associated with the function ρ. Also a Voronovskaya type result is obtained. Finally, we give some graphical examples for these operators and show that the new operators are more flexible in view of rate of convergence to the function f which depends on the selection of ρ, un,q and vn,q.