Applications of the deferred generalized de la Vall´ee Poussin means in approximation of continuous functions
DOI:
https://doi.org/10.24193/subbmath.2022.4.12Keywords:
Fourier series, generalized de la Vall´ee Poussin means, degree of approximation, modulus of continuity, Fourier series.Abstract
In this paper we have proved a theorem which show the degree of approximation of periodic functions by some generalized means of their Fourier series. In addition, our result is extended to two-dimensional setting as well.
Mathematics Subject Classification (2010): 42A10, 42A16.
Received 02 January 2020; Accepted 25 May 2020.
References
Acar, T., Mohiuddine, S.A., Statistical (C, 1)(E, 1) summability and Korovkin’s theorem, Filomat, 30(2016), no. 2, 387-393.
Agnew, R.P., The deferred Cesa`ro means, Ann. of Math. (2), 33(1932), no. 3, 413-421.
Al-Btoush, R., Al-Khaled, K., Approximation of periodic functions by Vallee Poussin sums, Hokkaido Math. J., 30(2001), no. 2, 269-282.
Alexits, G., U¨ber die Ann¨aherung einer stetigen Funktion durch die Cesaroschen Mittel ihrer Fourierreihe, (German), Math. Ann., 100(1928), 264-277.
Altomare, F., Iterates of Markov operators and constructive approximation of semigroups, Constr. Math. Anal., 2(1)(2019), 22-39.
Chandra, P., Degree of approximation by generalized de la Vall´ee-Poussin operators, Indian J. Math., 29(1987), no. 1, 85-88.
Garrancho, P., A general Korovkin result under generalized convergence, Constr. Math. Anal., 2(2)(2019), 81-88.
Holland, A.S.B., Sahney, B.N., Tzimbalario, J., On degree of approximation of a class of functions by means of Fourier series, Acta Sci. Math. (Szeged), 38(1976), no. 1-2, 69-72.
Khan, H.H., On the degree of approximation of functions belonging to class Lip (α, p), Indian J. Pure Appl. Math., 5(1974), no. 2, 132-136.
Leindler, L., On summability of Fourier series, Acta Sci. Math. (Szeged), 29(1968), 147-162.
Mohiuddine, S.A., Alotaibi, A., Abdullah. Statistical summability of double sequences through de la Vall´ee-Poussin mean in probabilistic normed spaces, Abstr. Appl. Anal. 2013, Art. ID 215612, 5 pp.
M´oricz, F., Rhoades, B.E., Approximation by No¨rlund means of double Fourier series to continuous functions in two variables, Constr. Approx., 3(1987), no. 3, 281-296.
Sezgek, S., Daˇgadur, I., Approximation by double deferred No¨rlund means of double Fourier series for Lipschitz functions, Cumhuriyet Sci. J., 39(2018), no. 3, 581-596.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Studia Universitatis Babeș-Bolyai Mathematica
![Creative Commons License](http://i.creativecommons.org/l/by-nc-nd/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.