Motivated by certain generalizations, in this paper we consider a new analogue of modified Szá sz-Mirakyan-Durrmeyer operators whose construction depends on a continuously differentiable, increasing and unbounded function τ with extra parameters μ and λ. Depending on the selection of μ and λ, these operators are more flexible than the modified Szá sz-Mirakyan-Durrmeyer operators while retaining their approximation properties. For these operators we give weighted approximation, Voronovskaya type theorem and quantitative estimates for the local approximation.
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