A New Class of Kantorovich-Type Operators

Year 2020, Volume: 3 Issue: 3, 116 - 124, 14.09.2020

Adrian Indrea Anamaria Indrea , Ovıdıu T. Pop

https://doi.org/10.33205/cma.773424

Cited By: 1

Abstract

The purpose of the paper called “A new class of Kantorovich-type operators”, as the title says, is to introduce a new class of Kantorovich-type operators with the property that the test functions $e_1$ and $e_2$ are reproduced. Furthermore, in our approach, an asymptotic type convergence theorem, a Voronovskaja type theorem and two error approximation theorems are given. As a conclusion, we make a comparison between the classical Kantorovich operators and the new class of Kantorovich - type operators.

Keywords

Bernstein polynomials, Kantorovich operators, King operators, fixed points

References

• Agratini, O., An asymptotic formula for a class of approximation processes of King’s type, Studia Sci. Math. Hungar., 47(2010), Number 4, 435-444
• Altomare, F., Campiti, M., Korovkin Type Approximation Theory and its Applications, Walter de Gruyter Studies in Math., Vol. 17, de Gruyter & Co., Berlin, 1994.
• Braica, P.I., Pop, O.T., Indrea, A.D., About a King-type operator, Appl. Math. Inf. Sci, No. 6 (1) (2012), 191-197.
• Indrea, A.D., Indrea, A.M., About a class of linear and positive Stancu-type operators, Acta Univ. Apulensis, 42 (2015), 1-8.
• Indrea, A.D., Indrea, A.M., Braica, P.I., Note on a Schurer-Stancu-type operator, Creative Mathematics and Informatics, 24 (2015), No. 1, 61 - 67.
• Indrea, A.D., Pop, O.T., Some general Baskakov type operators, Miskolc Math. Notes, 2 (2014), No. 2, 497-508.
• Kantorovich, L.V, Sur certain développments suivant les polynômes de la forme de S. Bernstein, I, II, C. R. Ac.ad. URSS (1930), 563-568, 595-600
• Pop, O. T., The generalization of Voronovskaja’s theorem for a class of liniar and positive operators, Rev. Anal. Numer. Théor. Approx., 34 (2005), No. 1, 79-91
• Shisha, O., Mond, B., The degree of convergence of linear positive operators, Proc. Nat. Acad. Sci. U.S.A., 60 (1968), 1196-1200.
• Stancu, D.D., On a generalization of the Bernstein polynomials, Studia Univ. "Babe¸s - Bolyai", Scr. Math - Phis 14, (1969), 31-45 (in Romanian)