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The purpose of this paper is to introduce Stancu variant of generalized Lupaş operators whose construction depends on a continuously differentiable, increasing and unbounded function ρ. Depending on the selection of γ and δ, these operators are more Ćexible than the generalized Lupaş operators while retaining their approximation properties. For these operators we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem. [ABSTRACT FROM AUTHOR]

We construct Kantorovich variant of generalized Szász-Mirakjan operators whose construction depends on a continuously differentiable, increasing and unbounded function τ. For these new operators we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to establish summation-integral type generalized Lupaş operators with weights of Beta basis functions which depends on μ having some properties. Primarily, for these new operators, we calculate moments and central moments, weighted approximation is discussed. Further, Voronovskaya type asymptotic theorem is proved. Finally, quantitative estimates for the local approximation is taken into consideration. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce q-analogues of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing, and unbounded function ρ. Depending on the selection of q, these operators provide more flexibility in approximation and the convergence is at least as fast as the generalized Lupaş operators, while retaining their approximation properties. For these operators, we give weighted approximations, Voronovskaja-type theorems, and quantitative estimates for the local approximation. [ABSTRACT FROM AUTHOR]