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On New Classes of Stancu-Kantorovich-Type Operators

Author

Listed:
  • 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)

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.

Suggested Citation

  • Bianca Ioana Vasian & Ștefan Lucian Garoiu & Cristina Maria Păcurar, 2021. "On New Classes of Stancu-Kantorovich-Type Operators," Mathematics, MDPI, vol. 9(11), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1235-:d:564142
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    References listed on IDEAS

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    1. Octavian Agratini, 2006. "Linear operators that preserve some test functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-11, July.
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