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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 τ with extra parameters μ μ and λ λ. Depending on the selection of μ μ and λ 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. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a Stancu type generalization of the Lupa¸s operators based on the q-integers. We investigate the rate of convergence of operators by mean of modulus of continuity and functions belonging to the Lipschitz class as well as Peetre’s K-functional. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences u m and v m of functions. 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, we prove Voronovskaya-type theorem, quantitative estimates for the local approximation. [ABSTRACT FROM AUTHOR]

In the present paper, Stancu type generalizations of the q-analog of Lupaş Bernstein operators with shifted knots are introduced. Some approximation results and rate of convergence for these operators are investigated. A Voronovskaja type theorem and local approximation results for the mentioned operators are studied. The extra parameters γ, δ, q, a and b provide more flexibility for approximation. [ABSTRACT FROM AUTHOR]