This paper presents the nonlinear maximum product type of univariate and bivariate Bernstein–Stancu operators and uses new definitions to investigate the approximation properties. The order of approximation obtained with the nonlinear maximum product type of operator sequences would be better than the degree of approximation of the known linear operator sequences.
Altomare, F., Campiti, M., Korovkin-Type Approximation Theory and Its Applications, Walter de Gruyter, Berlin, 1994.
Korovkin, P. P., Linear Operators and Approximation Theory, Hindustan Publ. Corp., India, 1960.
Stancu, D. D., Asupra unei generaliz˘ari a polinoamelor lui Bernstein, Studia Universitatis Babeş-Bolyai, 14(2) (1969), 31-45 (in Romanian).
Bede, B., Coroianu, L., Gal, S. G., Approximation and shape preserving properties of the Bernstein operator of max-product kind, Intern, J. Math. and Math. Sci., 26 pages (2009). doi:10.1155/2009/590589
Bede, B., Gal, S. G., Approximation by nonlinear Bernstein and Favard-Szasz-Mirakjan operators of max-product kind, Journal of Concrete and Applicable Mathematics, 8(2) (2010), 193-207.
Bede, B., Coroianu, L., Gal, S. G., Approximation by Max-Product Type Operators, Heidelberg, Springer, 2016.
Coroianu, L., Gal, S. G,. Approximation by nonlinear generalized sampling operators of max-product kind, Sampl. Theory Signal Image Process, 9 (2010), 59-75. https://doi.org/10.1007/BF03549524
Coroianu, L., Gal, S. G., Approximation by max-product sampling operators based on sinc-type kernels, Sampl. Theory Signal Image Process, 10 (2011), 211-230. https://doi.org/10.1007/BF03549542
Hildebrandt, T. H., Schoenberg, I. J., On linear functional operations and the moment problem, Ann. Math., 34(2) (1933), 317-328.
Butzer, P. L., On two-dimensional Bernstein polynomials, Can. J. Math., 5 (1953), 107-113.
Martinez, F. L., Some properties of two-dimensional Bernstein polynomials, Journal of approximation theory, 59(3) (1989), 300-306. https://doi.org/10.1016/0021-9045(89)90095-6
Kırcı Serenbay, S., Yavuz, H., Approximation Of Modified Bernstein-Stancu Operators Of Maximum-Product Type, presented at the İzdaş Kongre, Ankara, Turkey, 2021.
Acar, E., Kırcı Serenbay, S., Approximation by nonlinear q-Bernstein-Chlodowsky operators, TWMS J. App. and Eng. Math., 14(1) (2024), 42-51.
Acar, E., Özalp Guller, Ö., Kırcı Serenbay, S., Approximation by nonlinear Meyer-König and Zeller operators based on q-integers, International Journal of Mathematics and Computer in Engineering, 2(2) (2024), 71-82.
Acar, E., Kırcı Serenbay, S., Özalp Guller, Ö., Approximation by nonlinear Bernstein-Chlodowsky operators of Kantorovich type, Filomat, 37(14) (2023), 4621-4627. https://doi.org/10.2298/FIL2314621A
Özalp Guller, Ö., Acar, E., Kırcı Serenbay, S., Nonlinear bivariate Bernstein-Chlodowsky operators of maximum product type, Journal of Mathematics, (2022). https://doi.org/10.1155/2022/4742433
Acar, E., Holhoş, A., Kırcı Serenbay, S., Polynomial weighted approximation by Szasz-Mirakyan operators of max-product type, Kragujevac Journal of Mathematics, 49(3) (2022), 365-373. 10.46793/KgJMat2503.365A
Gairola, A. R., Singh, A., Rathour, L., Mishra, V. N., Improved rate of approximation by modification of Baskakov operator, Operators and Matrices, 16(4), (2022), 1097-1123. dx.doi.org/10.7153/oam-2022-16-72
Gairola, A. R., Maindola, S., Rathour, L., Mishra, L. N., Mishra, V. N., Better uniform approximation by new Bivariate Bernstein Operators, International Journal of Analysis and Applications, 20(60) (2022), 1-19. https://doi.org/10.28924/2291-8639-20-2022-60
Gairola, A. R., Bisht, N., Rathour, L., Mishra, L. N., Mishra, V. N., Order of approximation by a new univariate Kantorovich Type Operator, International Journal of Analysis and Applications, 21 (2023), 1-17. https://doi.org/10.28924/2291-8639-21-2023-106
Mishra, V. N., Khatri, K., Mishra, L. N., Deepmala, Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators, Journal of Inequalities and Applications, 586 (2013). https://doi.org/10.1186/1029-242X-2013-586
Yeşilnacar Binmar, A. K., Aproximation properties two biviariate maximum product type operators, Master Thesis, Harran University, Şanlıurfa, Türkiye, 2023.
Altomare, F., Campiti, M., Korovkin-Type Approximation Theory and Its Applications, Walter de Gruyter, Berlin, 1994.
Korovkin, P. P., Linear Operators and Approximation Theory, Hindustan Publ. Corp., India, 1960.
Stancu, D. D., Asupra unei generaliz˘ari a polinoamelor lui Bernstein, Studia Universitatis Babeş-Bolyai, 14(2) (1969), 31-45 (in Romanian).
Bede, B., Coroianu, L., Gal, S. G., Approximation and shape preserving properties of the Bernstein operator of max-product kind, Intern, J. Math. and Math. Sci., 26 pages (2009). doi:10.1155/2009/590589
Bede, B., Gal, S. G., Approximation by nonlinear Bernstein and Favard-Szasz-Mirakjan operators of max-product kind, Journal of Concrete and Applicable Mathematics, 8(2) (2010), 193-207.
Bede, B., Coroianu, L., Gal, S. G., Approximation by Max-Product Type Operators, Heidelberg, Springer, 2016.
Coroianu, L., Gal, S. G,. Approximation by nonlinear generalized sampling operators of max-product kind, Sampl. Theory Signal Image Process, 9 (2010), 59-75. https://doi.org/10.1007/BF03549524
Coroianu, L., Gal, S. G., Approximation by max-product sampling operators based on sinc-type kernels, Sampl. Theory Signal Image Process, 10 (2011), 211-230. https://doi.org/10.1007/BF03549542
Hildebrandt, T. H., Schoenberg, I. J., On linear functional operations and the moment problem, Ann. Math., 34(2) (1933), 317-328.
Butzer, P. L., On two-dimensional Bernstein polynomials, Can. J. Math., 5 (1953), 107-113.
Martinez, F. L., Some properties of two-dimensional Bernstein polynomials, Journal of approximation theory, 59(3) (1989), 300-306. https://doi.org/10.1016/0021-9045(89)90095-6
Kırcı Serenbay, S., Yavuz, H., Approximation Of Modified Bernstein-Stancu Operators Of Maximum-Product Type, presented at the İzdaş Kongre, Ankara, Turkey, 2021.
Acar, E., Kırcı Serenbay, S., Approximation by nonlinear q-Bernstein-Chlodowsky operators, TWMS J. App. and Eng. Math., 14(1) (2024), 42-51.
Acar, E., Özalp Guller, Ö., Kırcı Serenbay, S., Approximation by nonlinear Meyer-König and Zeller operators based on q-integers, International Journal of Mathematics and Computer in Engineering, 2(2) (2024), 71-82.
Acar, E., Kırcı Serenbay, S., Özalp Guller, Ö., Approximation by nonlinear Bernstein-Chlodowsky operators of Kantorovich type, Filomat, 37(14) (2023), 4621-4627. https://doi.org/10.2298/FIL2314621A
Özalp Guller, Ö., Acar, E., Kırcı Serenbay, S., Nonlinear bivariate Bernstein-Chlodowsky operators of maximum product type, Journal of Mathematics, (2022). https://doi.org/10.1155/2022/4742433
Acar, E., Holhoş, A., Kırcı Serenbay, S., Polynomial weighted approximation by Szasz-Mirakyan operators of max-product type, Kragujevac Journal of Mathematics, 49(3) (2022), 365-373. 10.46793/KgJMat2503.365A
Gairola, A. R., Singh, A., Rathour, L., Mishra, V. N., Improved rate of approximation by modification of Baskakov operator, Operators and Matrices, 16(4), (2022), 1097-1123. dx.doi.org/10.7153/oam-2022-16-72
Gairola, A. R., Maindola, S., Rathour, L., Mishra, L. N., Mishra, V. N., Better uniform approximation by new Bivariate Bernstein Operators, International Journal of Analysis and Applications, 20(60) (2022), 1-19. https://doi.org/10.28924/2291-8639-20-2022-60
Gairola, A. R., Bisht, N., Rathour, L., Mishra, L. N., Mishra, V. N., Order of approximation by a new univariate Kantorovich Type Operator, International Journal of Analysis and Applications, 21 (2023), 1-17. https://doi.org/10.28924/2291-8639-21-2023-106
Mishra, V. N., Khatri, K., Mishra, L. N., Deepmala, Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators, Journal of Inequalities and Applications, 586 (2013). https://doi.org/10.1186/1029-242X-2013-586
Yeşilnacar Binmar, A. K., Aproximation properties two biviariate maximum product type operators, Master Thesis, Harran University, Şanlıurfa, Türkiye, 2023.
Yeşilnacar Binmar, A. K., Acar, E., & Kırcı Serenbay, S. (n.d.). Approximation properties of the univariate and bivariate Bernstein-Stancu operators of max-product kind. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(3), 787-801. https://doi.org/10.31801/cfsuasmas.1452069
AMA
Yeşilnacar Binmar AK, Acar E, Kırcı Serenbay S. Approximation properties of the univariate and bivariate Bernstein-Stancu operators of max-product kind. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 73(3):787-801. doi:10.31801/cfsuasmas.1452069
Chicago
Yeşilnacar Binmar, Ayşe Kübra, Ecem Acar, and Sevilay Kırcı Serenbay. “Approximation Properties of the Univariate and Bivariate Bernstein-Stancu Operators of Max-Product Kind”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, no. 3 n.d.: 787-801. https://doi.org/10.31801/cfsuasmas.1452069.
EndNote
Yeşilnacar Binmar AK, Acar E, Kırcı Serenbay S Approximation properties of the univariate and bivariate Bernstein-Stancu operators of max-product kind. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 3 787–801.
IEEE
A. K. Yeşilnacar Binmar, E. Acar, and S. Kırcı Serenbay, “Approximation properties of the univariate and bivariate Bernstein-Stancu operators of max-product kind”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 73, no. 3, pp. 787–801, doi: 10.31801/cfsuasmas.1452069.
ISNAD
Yeşilnacar Binmar, Ayşe Kübra et al. “Approximation Properties of the Univariate and Bivariate Bernstein-Stancu Operators of Max-Product Kind”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/3 (n.d.), 787-801. https://doi.org/10.31801/cfsuasmas.1452069.
JAMA
Yeşilnacar Binmar AK, Acar E, Kırcı Serenbay S. Approximation properties of the univariate and bivariate Bernstein-Stancu operators of max-product kind. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.;73:787–801.
MLA
Yeşilnacar Binmar, Ayşe Kübra et al. “Approximation Properties of the Univariate and Bivariate Bernstein-Stancu Operators of Max-Product Kind”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 73, no. 3, pp. 787-01, doi:10.31801/cfsuasmas.1452069.
Vancouver
Yeşilnacar Binmar AK, Acar E, Kırcı Serenbay S. Approximation properties of the univariate and bivariate Bernstein-Stancu operators of max-product kind. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 73(3):787-801.