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Cesàro summability and Lebesgue points of higher dimensional Fourier series
New approximation properties of the Bernstein max-min operators and Bernstein max-product operators
Department of Mathematics and Computer Science, University of Oradea, Universitatii 1, 410087, Oradea, Romania |
In this paper we put in evidence localization results for the so-called Bernstein max-min operators and a property of translation for the Bernstein max-product operators.
References:
| [1] |
A. G. Anastassiou, L. Coroianu and S. G. Gal,
Approximation by a nonlinear Cardaliaguet-Euvrard neural network operator of max-product kind, J. Comp. Anal. Appl., 12 (2010), 396-406.
|
| [2] |
B. Bede, L. Coroianu and S. G. Gal,
Approximation and shape preserving properties of the Bernstein operator of max-product kind, Intern. J. Math. Math. Sci., 2009 (2009), 590589.
doi: 10.1155/2009/590589. |
| [3] |
B. Bede, L. Coroianu and S. G. Gal,
Approximation and shape preserving properties of the nonlinear Meyer-König and Zeller operator of max-product kind, Numer. Funct. Anal. Optim., 31 (2010), 232-253.
doi: 10.1080/01630561003757686. |
| [4] |
B. Bede, L. Coroianu and S. G. Gal, Approximation by Max-Product Type Operators, Springer, [Cham], 2016.
doi: 10.1007/978-3-319-34189-7. |
| [5] |
B. Bede, H. Nobuhara, J. Fodor and K. Hirota,
Max-product Shepard approximation operators,, J. Adv. Comput. Intell. Inform., 10 (2006), 494-497.
doi: 10.20965/jaciii.2006.p0494. |
| [6] |
L. Coroianu, D. Costarelli, S. G. Gal and G. Vinti,
Approximation by max-product sampling Kantorovich operators with generalized kernels, Anal. Appl. (Singap.), 19 (2021), 219-244.
doi: 10.1142/S0219530519500155. |
| [7] |
L. Coroianu, D. Costarelli, S. G. Gal and G. Vinti,
Connections between the approximation orders of positive linear operators and their max-product counterparts, Numer. Funct. Anal. Optim., 42 (2021), 1263-1286.
doi: 10.1080/01630563.2021.1954018. |
| [8] |
L. Coroianu, D. Costarelli, S. G. Gal and G. Vinti,
The max-product generalized sampling operators: Convergence and quantitative estimates,, Appl. Math. Comput., 355 (2019), 173-183.
doi: 10.1016/j.amc.2019.02.076. |
| [9] |
L. Coroianu and S. G. Gal,
Approximation by max-product Lagrange interpolation operators, Stud. Univ. Babeş -Bolyai Math., 56 (2011), 315-325.
|
| [10] |
L. Coroianu and S. G. Gal,
Classes of functions with improved estimates in approximation by the max-product Bernstein operator,, Anal. Appl. (Singap.), 9 (2011), 249-274.
doi: 10.1142/S0219530511001856. |
| [11] |
L. Coroianu and S. G. Gal,
Localization results for the Bernstein max-product operator,, Appl. Math. Comput., 231 (2014), 73-78.
doi: 10.1016/j.amc.2013.12.190. |
| [12] |
L. Coroianu, S. G. Gal and B. Bede,
Approximation of fuzzy numbers by Bernstein operators of max-product kind,, Fuzzy Set. Syst., 257 (2014), 41-66.
doi: 10.1016/j.fss.2013.04.010. |
| [13] |
D. Costarelli, A. R. Sambucini and G. Vinti,
Convergence in Orlicz spaces by means of the multivariate max-product neural network operators of the Kantorovich type and applications,, Neural Comput. Appl., 31 (2019), 5069-5078.
doi: 10.1007/s00521-018-03998-6. |
| [14] |
D. Costarelli and G. Vinti,
Max-product neural network and quasi-interpolation operators activated by sigmoidal functions,, J. Approx. Theory, 209 (2016), 1-22.
doi: 10.1016/j.jat.2016.05.001. |
| [15] |
S. G. Gal, Shape-Preserving Approximation by Real and Complex Polynomials, Birkhäuser, Boston-Basel-Berlin, 2008.
doi: 10.1007/978-0-8176-4703-2. |
| [16] |
T. Y. Gökçer and O. Duman,
Approximation by max-min operators: A general theory and its applications,, Fuzzy Sets and Systems, 394 (2020), 146-161.
doi: 10.1016/j.fss.2019.11.007. |
| [17] |
T. Y. Gökcer and O. Duman,
Summation process by max-product operators,, Computational Analysis, 155 (2016), 59-67.
doi: 10.1007/978-3-319-28443-9_4. |
| [18] |
S. Y. Güngör and N. Ispir,
Approximation by Bernstein-Chlodowsky operators of max-product kind., Math. Commun., 23 (2018), 205-225.
|
| [19] |
A. Holhoş,
Weighted approximation of functions by Favard operators of max-product type,, Period. Math. Hungar., 77 (2018), 340-346.
doi: 10.1007/s10998-018-0249-9. |
| [20] |
A. Holhoş,
Weighted approximation of functions by Meyer-K önig and Zeller operators of max-product type,, Numer. Funct. Anal. Optim., 39 (2018), 689-703.
doi: 10.1080/01630563.2017.1413386. |
| [21] |
S. Karakus and K. Demirci,
Statistical $\sigma $-approximation to max-product operators,, Comput. Math. Appl., 61 (2011), 1024-1031.
doi: 10.1016/j.camwa.2010.12.052. |
show all references
References:
| [1] |
A. G. Anastassiou, L. Coroianu and S. G. Gal,
Approximation by a nonlinear Cardaliaguet-Euvrard neural network operator of max-product kind, J. Comp. Anal. Appl., 12 (2010), 396-406.
|
| [2] |
B. Bede, L. Coroianu and S. G. Gal,
Approximation and shape preserving properties of the Bernstein operator of max-product kind, Intern. J. Math. Math. Sci., 2009 (2009), 590589.
doi: 10.1155/2009/590589. |
| [3] |
B. Bede, L. Coroianu and S. G. Gal,
Approximation and shape preserving properties of the nonlinear Meyer-König and Zeller operator of max-product kind, Numer. Funct. Anal. Optim., 31 (2010), 232-253.
doi: 10.1080/01630561003757686. |
| [4] |
B. Bede, L. Coroianu and S. G. Gal, Approximation by Max-Product Type Operators, Springer, [Cham], 2016.
doi: 10.1007/978-3-319-34189-7. |
| [5] |
B. Bede, H. Nobuhara, J. Fodor and K. Hirota,
Max-product Shepard approximation operators,, J. Adv. Comput. Intell. Inform., 10 (2006), 494-497.
doi: 10.20965/jaciii.2006.p0494. |
| [6] |
L. Coroianu, D. Costarelli, S. G. Gal and G. Vinti,
Approximation by max-product sampling Kantorovich operators with generalized kernels, Anal. Appl. (Singap.), 19 (2021), 219-244.
doi: 10.1142/S0219530519500155. |
| [7] |
L. Coroianu, D. Costarelli, S. G. Gal and G. Vinti,
Connections between the approximation orders of positive linear operators and their max-product counterparts, Numer. Funct. Anal. Optim., 42 (2021), 1263-1286.
doi: 10.1080/01630563.2021.1954018. |
| [8] |
L. Coroianu, D. Costarelli, S. G. Gal and G. Vinti,
The max-product generalized sampling operators: Convergence and quantitative estimates,, Appl. Math. Comput., 355 (2019), 173-183.
doi: 10.1016/j.amc.2019.02.076. |
| [9] |
L. Coroianu and S. G. Gal,
Approximation by max-product Lagrange interpolation operators, Stud. Univ. Babeş -Bolyai Math., 56 (2011), 315-325.
|
| [10] |
L. Coroianu and S. G. Gal,
Classes of functions with improved estimates in approximation by the max-product Bernstein operator,, Anal. Appl. (Singap.), 9 (2011), 249-274.
doi: 10.1142/S0219530511001856. |
| [11] |
L. Coroianu and S. G. Gal,
Localization results for the Bernstein max-product operator,, Appl. Math. Comput., 231 (2014), 73-78.
doi: 10.1016/j.amc.2013.12.190. |
| [12] |
L. Coroianu, S. G. Gal and B. Bede,
Approximation of fuzzy numbers by Bernstein operators of max-product kind,, Fuzzy Set. Syst., 257 (2014), 41-66.
doi: 10.1016/j.fss.2013.04.010. |
| [13] |
D. Costarelli, A. R. Sambucini and G. Vinti,
Convergence in Orlicz spaces by means of the multivariate max-product neural network operators of the Kantorovich type and applications,, Neural Comput. Appl., 31 (2019), 5069-5078.
doi: 10.1007/s00521-018-03998-6. |
| [14] |
D. Costarelli and G. Vinti,
Max-product neural network and quasi-interpolation operators activated by sigmoidal functions,, J. Approx. Theory, 209 (2016), 1-22.
doi: 10.1016/j.jat.2016.05.001. |
| [15] |
S. G. Gal, Shape-Preserving Approximation by Real and Complex Polynomials, Birkhäuser, Boston-Basel-Berlin, 2008.
doi: 10.1007/978-0-8176-4703-2. |
| [16] |
T. Y. Gökçer and O. Duman,
Approximation by max-min operators: A general theory and its applications,, Fuzzy Sets and Systems, 394 (2020), 146-161.
doi: 10.1016/j.fss.2019.11.007. |
| [17] |
T. Y. Gökcer and O. Duman,
Summation process by max-product operators,, Computational Analysis, 155 (2016), 59-67.
doi: 10.1007/978-3-319-28443-9_4. |
| [18] |
S. Y. Güngör and N. Ispir,
Approximation by Bernstein-Chlodowsky operators of max-product kind., Math. Commun., 23 (2018), 205-225.
|
| [19] |
A. Holhoş,
Weighted approximation of functions by Favard operators of max-product type,, Period. Math. Hungar., 77 (2018), 340-346.
doi: 10.1007/s10998-018-0249-9. |
| [20] |
A. Holhoş,
Weighted approximation of functions by Meyer-K önig and Zeller operators of max-product type,, Numer. Funct. Anal. Optim., 39 (2018), 689-703.
doi: 10.1080/01630563.2017.1413386. |
| [21] |
S. Karakus and K. Demirci,
Statistical $\sigma $-approximation to max-product operators,, Comput. Math. Appl., 61 (2011), 1024-1031.
doi: 10.1016/j.camwa.2010.12.052. |
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