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On a New Class of Stancu-Kantorovich-Type Operators
Version 1
: Received: 8 May 2021 / Approved: 10 May 2021 / Online: 10 May 2021 (13:48:54 CEST)
A peer-reviewed article of this Preprint also exists.
Vasian, B.I.; Garoiu, Ș.L.; Păcurar, C.M. On New Classes of Stancu-Kantorovich-Type Operators. Mathematics 2021, 9, 1235. Vasian, B.I.; Garoiu, Ș.L.; Păcurar, C.M. On New Classes of Stancu-Kantorovich-Type Operators. Mathematics 2021, 9, 1235.
Abstract
The present paper introduces a new class of Stancu-Kantorovich operators constructed in the King sense. For this class of operators we establish some convergence results, error estimations theorems and graphical properties of approximation for the cases 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 new class of operators introduced in this paper is a genuine generalization of the class introduced by Indrea et al. (see Indrea A., Indrea A., Pop O. A New Class of Kantorovich-Type Operators, Constructive Mathematical Analysis).
Keywords
Stancu operators; Kantorovich operators; Stancu-Kantorovich operators; King-type operators; approximation by positive linear operators
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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