Year 2019,
, 57 - 63, 01.06.2019
Grazyna Krech
,
Ireneusz Krech
References
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operators. Math. Comput. Modelling 50(7-8) (2009), 984–998.
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(2008), 2501–2515.
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- [12] L. R. Bragg: The radial heat polynomials and related functions. Trans. Amer. Math. Soc. 119 (1965), 270–290.
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York 1971.
- [14] B. Firlej and L. Rempulska: On some singular integrals in Hölder spaces. Mat. Nachr. 170 (1994), 93–100.
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Commun. Fac. Sci. Univ. Ank., Series A1 30 (1981), 55–62.
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integrals. Cubo 13(3) (2011), 17–48.
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Math. Nachr. 149 (1990), 117–124.
- [19] L. Rempulska and Z.Walczak: On modified Picard and Gauss-Weierstrass singular integrals. Ukrainian Math. J. 57(11)
(2005), 1844-1852.
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w Krakowie, Prace Matematyczne 17 (2000), 251–263.
On Some Bivariate Gauss-Weierstrass Operators
Year 2019,
, 57 - 63, 01.06.2019
Grazyna Krech
,
Ireneusz Krech
Abstract
The aim of the paper is to investigate the approximation properties of bivariate generalization of Gauss-Weierstrass operators associated with the Riemann-Liouville operator. In particular, the approximation error will be estimated by these operators in the space of functions defined and continuous in the half-plane $(0, \infty) \times \mathbb{R}$, and bounded by certain exponential functions.
References
- [1] G. A. Anastassiou and A. Aral: On Gauss-Weierstrass type integral operators. Demonstratio Math. 43(4) (2010), 841–
849.
- [2] G. A. Anastassiou and O. Duman: Statistical approximation by double complex Gauss-Weierstrass integral operators.
Appl. Math. Letters 24(4) (2011), 438–443.
- [3] G. A. Anastassiou and O. Duman: Statistical Lp-approximation by double Gauss-Weierstrass singular integral operators.
Comput. Math. Appl. 59(6) (2010), 1985–1999.
- [4] G. A. Anastassiou and R. A. Mezei: Global smoothness and uniform convergence of smooth Gauss-Weierstrass singular
operators. Math. Comput. Modelling 50(7-8) (2009), 984–998.
- [5] A. Aral: On a generalized $\lambda$-Gauss Weierstrass singular integral. Fasc. Math. 35 (2005), 23–33.
- [6] A. Aral: On the generalized Picard and Gauss Weierstrass singular integrals, J. Comput. Anal. Appl. 8(3) (2006), 246–
261.
- [7] A. Aral: Pointwise approximation by the generalization of Picard and Gauss-Weierstrass singular integrals. J. Concr. Appl.
Math. 6 (2008), 327–339.
- [8] A. Aral and S. G. Gal: q-generalizations of the Picard and Gauss-Weierstrass singular integrals. Taiwanese J. Math. 12(9)
(2008), 2501–2515.
- [9] B. Armi and L. T. Rachdi: The Littlewood-Paley g-function associated with the Riemann-Liouville operator. Ann. Univ.
Paedagog. Crac. Stud. Math. 12 (2013), 31–58.
- [10] C. Baccar, N. B. Hamadi and L. T. Rachdi: Inversion formulas for Riemann-Liouville transform and its dual associated
with singular partial differential operators. Int. J. Math. Math. Sci. (2006), Art. ID 86238, 26.
- [11] K. Bogalska, E. Gojka, M. Grudek and L. Rempulska: The Picard and the Gauss-Weierstrass singular integrals of
function of two variables. Le Mathematiche LII (1997), 71–85.
- [12] L. R. Bragg: The radial heat polynomials and related functions. Trans. Amer. Math. Soc. 119 (1965), 270–290.
- [13] P. L. Butzer and R. J. Nessel: Fourier Analysis and Approximation. Vol 1, Birkhauser, Basel and Academic Press, New
York 1971.
- [14] B. Firlej and L. Rempulska: On some singular integrals in Hölder spaces. Mat. Nachr. 170 (1994), 93–100.
- [15] F. H. Jackson: On a q-definite integrals. Quart. J. Pure Appl. Math. 41 (1910), 193–203.
- [16] A. Khan and S. Umar: On the order of approximation to a function by generalized Gauss-Weierstrass singular integrals.
Commun. Fac. Sci. Univ. Ank., Series A1 30 (1981), 55–62.
- [17] R. A. Mezei: Applications and Lipschitz results of approximation by smooth Picard and Gauss-Weierstrass type singular
integrals. Cubo 13(3) (2011), 17–48.
- [18] R. N. Mohapatra and R. S. Rodriguez: On the rate of convergence of singular integrals for Hölder continuous functions.
Math. Nachr. 149 (1990), 117–124.
- [19] L. Rempulska and Z.Walczak: On modified Picard and Gauss-Weierstrass singular integrals. Ukrainian Math. J. 57(11)
(2005), 1844-1852.
- [20] E. Wachnicki: On a Gauss-Weierstrass generalized integral. Rocznik Naukowo-Dydaktyczny Akademii Pedagogicznej
w Krakowie, Prace Matematyczne 17 (2000), 251–263.