Approximation by Max-Product operators

• Autorzy: Anastassiou G. A.

Identyfikatory

DOI

10.1515/fascmath-2018-0001

• Języki publikacji: EN

Abstrakty

EN

Here we study the approximation of functions by a great variety of Max-Product operators under differentiability. These are positive sublinear operators. Our study is based on our general results about positive sublinear operators. We produce Jackson type inequalities under initial conditions. So our approach is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of a high order derivative of the function under approximation. We improve known related results which do not use smoothness of functions.

Słowa kluczowe

EN

positive sublinear operators; Max-product operators; modulus of continuity

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2018
• Tom: Nr 60
• Strony: 5--28
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Anastassiou G. A.

• Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A

Bibliografia

• [1] Anastassiou G., Approximation by Sublinear Operators, submitted, 2017.
• [2] Anastassiou G., Coroianu L., Gal S., Approximation by a nonlinear Cardaliaguet-Euvrard neural network operator of max-product kind, J. Computational Analysis & Applications, 12(2)(2010), 396-406.
• [3] Bede B., Coroianu L., Gal S., Approximation by Max-Product type Operators, Springer, Heidelberg, New York, 2016.
• [4] Fejér L., Über Interpolation, Göttingen Nachrichten, (1916), 66-91.
• [5] Moldovan E., Observations sur certains procedes d’interpolation généralisés, (Romanian, Russian and French summaries), Acad. Republicii Pop. Romane Bul. Stiint. Sect. Stiint. Mat. Fiz., 6, (1954), 477-482.
• [6] Popoyiciu T., On the proof of Weierstrass’ theorem with the interpolation polynomials, Acad. Republicii Pop. Romane, ”Lucrarile sesiunii generale stiintifice din 2-12 Iunie 1950”. 1-4(1950), 1664-1667 (in Romanian).

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).