Abstract
In this paper, we establish a link between the Szász-Durrmeyer type operators and multiple Appell polynomials. We study a quantitative-Voronovskaya type theorem in terms of weighted modulus of smoothness using sixth order central moment and Grüss-Voronovskaya type theorem. We also establish a local approximation theorem by means of the Steklov means in terms of the first and the second order modulus of continuity and Voronovskaya type asymtotic theorem. Further, we discuss the degree of approximation by means of the weighted spaces. Lastly, we find the rate of approximation of functions having a derivative of bounded variation.
Highlights
For f ∈ C(R+ ) and x ∈ R+ (R+ = [, ∞)), Szász [ ] introduced the well-known operators Sn(f ; x) = e–nx ∞k f k! k, n ( ) k=such that Sn(|f |; x) < ∞
Several generalizations of Szász operators have been introduced in the literature and authors have studied their approximation properties
In [ ], the author considered Baskakov-Szász type operators and studied the rate of convergence for absolutely continuous functions having a derivative equivalent with a function of bounded variation
Summary
Several generalizations of Szász operators have been introduced in the literature and authors have studied their approximation properties. In [ ], the author considered Baskakov-Szász type operators and studied the rate of convergence for absolutely continuous functions having a derivative equivalent with a function of bounded variation. In [ ], the authors introduced the q-Baskakov-Durrmeyer type operators and studied the rate of convergence and the weighted approximation properties.
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