Approximation Properties of Parametric Kantorovich-Type Operators on Half-Bounded Intervals

Hui Dong and Qiulan Qi ()
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Hui Dong: School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
Qiulan Qi: School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China

Mathematics, 2023, vol. 11, issue 24, 1-15

Abstract: The main purpose of this paper is to introduce a new family of parametric Kantorovichtype operators on the half-bounded interval. The convergence properties of these new operators are investigated. The Voronovskaja-type weak inverse theorem and the rate of uniform convergence are obtained. Furthermore, we obtain some shape preserving properties of these operators, including monotonicity, convexity, starshapeness, and semi-additivity preserving properties. Finally, some numerical illustrative examples show that these new operators have a better approximation performance than the classical ones.

Keywords: Kantorovich-type operators; positive theorem; the Voronovskaja type weak inverse theorem; shape preserving property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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