On better approximation order for the max-product Meyer-König and Zeller operator
Bede et al. (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), no. 3, 232–253) defined the max-product Meyer-König and Zeller operator. They examined the appro...
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De Gruyter
2025-07-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2025-0127 |
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| _version_ | 1839581956013031424 |
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| author | Çit Sezin Doğru Ogün |
| author_facet | Çit Sezin Doğru Ogün |
| author_sort | Çit Sezin |
| collection | DOAJ |
| description | Bede et al. (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), no. 3, 232–253) defined the max-product Meyer-König and Zeller operator. They examined the approximation and shape preserving properties of this operator, and they found the order of approximation to be y(1−y)m\frac{\sqrt{y}(1-y)}{\sqrt{m}} by the modulus of continuity and claimed that this order of approximation could only be improved in certain subclasses of the functions. In contrast to this claim, we demonstrate that we can obtain a better order of approximation without reducing the function class (by the classical modulus of continuity). We find the degree of approximation to be (1−y)y1αm1−1α\frac{(1-y){y}^{\tfrac{1}{\alpha }}}{{m}^{1-\tfrac{1}{\alpha }}}, α=2,3,…\alpha =2,3,\ldots . Since 1−1α1-\frac{1}{\alpha } tends to 1 for enough big α\alpha , we improve this degree of approximation. |
| format | Article |
| id | doaj-art-c7595d618ddb45dd82d53c58ed8c4db0 |
| institution | Matheson Library |
| issn | 2391-4661 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-c7595d618ddb45dd82d53c58ed8c4db02025-08-04T09:39:14ZengDe GruyterDemonstratio Mathematica2391-46612025-07-0158180482010.1515/dema-2025-0127On better approximation order for the max-product Meyer-König and Zeller operatorÇit Sezin0Doğru Ogün1Department of Mathematics, Gazi University, Ankara, 06560, TurkeyDepartment of Mathematics, Gazi University, Ankara, 06560, TurkeyBede et al. (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), no. 3, 232–253) defined the max-product Meyer-König and Zeller operator. They examined the approximation and shape preserving properties of this operator, and they found the order of approximation to be y(1−y)m\frac{\sqrt{y}(1-y)}{\sqrt{m}} by the modulus of continuity and claimed that this order of approximation could only be improved in certain subclasses of the functions. In contrast to this claim, we demonstrate that we can obtain a better order of approximation without reducing the function class (by the classical modulus of continuity). We find the degree of approximation to be (1−y)y1αm1−1α\frac{(1-y){y}^{\tfrac{1}{\alpha }}}{{m}^{1-\tfrac{1}{\alpha }}}, α=2,3,…\alpha =2,3,\ldots . Since 1−1α1-\frac{1}{\alpha } tends to 1 for enough big α\alpha , we improve this degree of approximation.https://doi.org/10.1515/dema-2025-0127nonlinear meyer-könig and zeller operatormax-product kind operatorsmodulus of continuity41a1041a2541a36 |
| spellingShingle | Çit Sezin Doğru Ogün On better approximation order for the max-product Meyer-König and Zeller operator Demonstratio Mathematica nonlinear meyer-könig and zeller operator max-product kind operators modulus of continuity 41a10 41a25 41a36 |
| title | On better approximation order for the max-product Meyer-König and Zeller operator |
| title_full | On better approximation order for the max-product Meyer-König and Zeller operator |
| title_fullStr | On better approximation order for the max-product Meyer-König and Zeller operator |
| title_full_unstemmed | On better approximation order for the max-product Meyer-König and Zeller operator |
| title_short | On better approximation order for the max-product Meyer-König and Zeller operator |
| title_sort | on better approximation order for the max product meyer konig and zeller operator |
| topic | nonlinear meyer-könig and zeller operator max-product kind operators modulus of continuity 41a10 41a25 41a36 |
| url | https://doi.org/10.1515/dema-2025-0127 |
| work_keys_str_mv | AT citsezin onbetterapproximationorderforthemaxproductmeyerkonigandzelleroperator AT dogruogun onbetterapproximationorderforthemaxproductmeyerkonigandzelleroperator |