On New Classes of Stancu-Kantorovich-Type Operators

Bianca Ioana Vasian, Ștefan Lucian Garoiu and Cristina Maria Păcurar
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Bianca Ioana Vasian: Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Transilvania University of Brașov, Iuliu Maniu Str., 500090 Brașov, Romania
Ștefan Lucian Garoiu: Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Transilvania University of Brașov, Iuliu Maniu Str., 500090 Brașov, Romania
Cristina Maria Păcurar: Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Transilvania University of Brașov, Iuliu Maniu Str., 500090 Brașov, Romania

Mathematics, 2021, vol. 9, issue 11, 1-16

Abstract: The present paper introduces new classes of Stancu–Kantorovich operators constructed in the King sense. For these classes of operators, we establish some convergence results, error estimations theorems and graphical properties of approximation for the classes considered, namely, operators that preserve the test functions e 0 ( x ) = 1 and e 1 ( x ) = x , e 0 ( x ) = 1 and e 2 ( x ) = x 2 , as well as e 1 ( x ) = x and e 2 ( x ) = x 2 . The class of operators that preserve the test functions e 1 ( x ) = x and e 2 ( x ) = x 2 is a genuine generalization of the class introduced by Indrea et al. in their paper “A New Class of Kantorovich-Type Operators”, published in Constr. Math. Anal.

Keywords: Stancu operators; Kantorovich operators; Stancu–Kantorovich operators; King-type operators; approximation by positive linear operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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