On trigonometric approximation of functions in the Lq norm

• Autorzy: Mohapatra R. N. , Szal B.

Identyfikatory

DOI

10.1515/dema-2018-0004

• Języki publikacji: EN

Abstrakty

EN

In this paper we obtain a degree of approximation of functions in Lq by operators associated with their Fourier series using integral modulus of continuity. These results generalize many known results and are proved under less stringent conditions on the infinite matrix.

Słowa kluczowe

EN

class Lip (β, q); trigonometric approximation; Lq norm

PL

aproksymacja trygonometryczna; norma Lq

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2018
• Tom: Vol. 51, nr 1
• Strony: 17--26
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Mohapatra R. N.

• University of Central Florida, Orlando, FL 32816, USA

autor

Szal B.

• University of Zielona Góra, Faculty of Mathematics, Computer Science and Econometrics, 65-516 Zielona Góra, ul. Szafrana 4a, Poland

Bibliografia

• [1] Leindler L., On the degree of approximation of continuous functions, Acta Math. Hungar., 2004, 104(1-2), 105-113
• [2] Quade E. S., Trigonometric approximation in the mean, Duke Math. J., 1937, 3, 529-543
• [3] Chandra P., Approximation by Nörlund operators, Mat. Vesnik, 1986, 38, 263-269
• [4] Chandra P., Functions of classes Lp and Lip (α, p) and their Riesz means, Riv. Mat. Univ. Parma, 1986, 12(4), 275-282
• [5] Chandra P., A note on degree of approximation by Nörlund and Riesz operators, Mat. Vesnik, 1990, 42, 9-10
• [6] Mohapatra R. N., Russell D. C., Some direct and inverse theorem in approximation of functions, J. Austral. Math. Soc. (Ser. A), 1983, 34, 143-154
• [7] Sahney B. N., Rao V. V., Error bounds in the approximation of functions, Bull. Austral. Math. Soc., 1972, 6, 11-18
• [8] Chandra P., Trigonometric approximation of functions in Lp norm, J. Math. Anal. Appl., 2002, 275, 13-26
• [9] Mittal M. L., Rhoades B. E., Mishra V. N., Singh U., Using infinite matrices to approximate functions of class Lip (α, p) using trigonometric polynomials, J. Math. Anal. Appl., 2007, 326, 667-676
• [10] Szal B., Trigonometric approximation by Nörlund type means in Lp norm, Comment. Math. Univ. Carolin., 2009, 50(4), 575-589

Uwagi

PL

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