Abstract
We extend the results of Xh.Z. Krasniqi [Acta Comment. Univ. Tartu. Math., 17:89–101, 2013] and the authors [Acta Comment. Univ. Tartu. Math., 13:11–24, 2019] to the case where in the measures of estimations r-differences of the entries are used.
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W. Łenski and B. Szal, Approximation of functions belonging to the class Lp(ω) by linear operators, Acta Comment. Univ. Tartu. Math., 13:11–24, 2009.
Xh. Z. Krasniqi, Slight extensions of some theorems on the rate of pointwise approximation of functions from some subclasses of Lp, Acta Comment. Univ. Tartu. Math., 17:89–101, 2013.
L. N. Mishra, On Existence and Behavior of Solutions to Some Nonlinear Integral Equations with Applications, PhD thesis, National Institute of Technology Silchar, India, 2017.
L. N. Mishra, V. N. Mishra, K. Khatri, and Deepmala, On the trigonometric approximation of signals belonging to generalized weighted Lipschitz W(Lr, ξ(t)) (r ⩾ 1)-class by matrix (C1∙Np) operator of conjugate series of its Fourier series, Appl. Math. Comput., 237:252–263, 2014.
V. N. Mishra, Some Problems on Approximations of Functions in Banach Spaces, PhD thesis, Indian Institute of Technology Roorkee, India, 2007.
V. N. Mishra, K. Khatri, L. N. Mishra, and Deepmala, Trigonometric approximation of periodic signals belonging to generalized weighted Lipschitz W(Lr, ξ(t)) (r ⩾ 1)-class by Nörlund–Euler (N, pn)(E, q) operator of conjugate series of its Fourier series, J. Class. Anal., 5(2):91–105, 2014, available from: https://doi.org/10.7153/jca-05-08.
V. N. Mishra and L. N. Mishra, Trigonometric approximation of signals (functions) in Lp (p ⩾ 1)-norm, Int. J. Contemp. Math. Sci., 7(19):909–918, 2012.
B. Szal, A new class of numerical sequences and its applications to uniform convergence of sine series, Math. Nachr., 284(14–15):1985–2002, 2011.
B. Szal, On L-convergence of trigonometric series, J. Math. Anal. Appl., 373:449–463, 2011.
A. Zygmund, Trigonometric Series, Cambridge Univ. Press, Cambridge, 2002.
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Łenski, W., Szal, B. Pointwise approximation of functions by matrix operators of their Fourier series with r-differences of the entries. Lith Math J 60, 494–512 (2020). https://doi.org/10.1007/s10986-020-09501-w
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DOI: https://doi.org/10.1007/s10986-020-09501-w