Approximation by nonlinear Meyer-König and Zeller operators based on q-integers
References
- Gupta V., Rassias M.T., Moments of Linear Positive Operators and Approximation, Springer, 2019.
- Gal S.G., Shape-Preserving Approximation by Real and Complex Polynomials, Birkhäuser, Boston, 2008.
- Lupaş A., A q-analogue of the Bernstein operator, Seminar on Numerical and Statistical Calculus, University of Cluj-Napoca, 9, 85–92, 1987.
- Phillips G.M., Bernstein polynomials based on the q-integers, Annals of Numerical Mathematics, 4(1–4), 511–518, 1997.
- Phillips G.M., A generalization of the Bernstein polynomials based on the q-integers, The Anziam Journal, 42(1), 79–86, 2000.
- Oruç H., Tuncer N., On the convergence and iterates of q-Bernstein polynomials, Journal of Approximation Theory, 117(2), 301–313, 2002.
- Ostrovska S., q-Bernstein polynomials and their iterates, Journal of Approximation Theory, 123(2), 232–255, 2003.
- Derriennic M.M., Modified Bernstein polynomials and Jacobi polynomials in q-calculus, Rendiconti del Circolo Matematico di Palermo, 2(76), 269–290, 2005.
- Finta Z., Gupta V., Approximation by q-Durrmeyer operators, Journal of Applied Mathematics and Computing, 29, 401–415, 2009.
- Khan K., Lobiyal D.K., Bèzier curves based on Lupaş (p,q)-analogue of Bernstein functions in CAGD, Journal of Computational and Applied Mathematics, 317, 458–477, 2017.
- Khan K., Lobiyal D.K., Kilicman A., Bèzier curves and surfaces based on modified Bernstein polynomials, Azerbaijan Journal of Mathematics, 9(1), 3–21, 2019.
- Farouki R.T., The Bernstein polynomial basis: A centennial retrospective, Computer Aided Geometric Design, 29(6), 379–419, 2012.
- Bede B., Coroianu L., Gal S.G., Approximation and shape preserving properties of the Bernstein operator of max-product kind, International Journal of Mathematics and Mathematical Sciences, 2009(ID:590589), 26 pages, 2009.
- Acar E., Karahan D., Kırcı Serenbay S., Approximation for the Bernstein operator of max-product kind in symmetric range, Khayyam Journal of Mathematics, 6(2), 257–273, 2020.
- Özalp Güller Ö., Acar E., Kırcı Serenbay S., Nonlinear bivariate Bernstein-Chlodowsky operators of maximum product type, Journal of Mathematics, 2022(ID:4742433), 11 pages, 2022.
- Özalp Güller Ö., Acar E., Kırcı Serenbay S., Some new theorems on the approximation of maximum product type of multivariate nonlinear Bernstein-Chlodowsky operators, Advances in Operator Theory, 7(27), 1–15, 2022.
- Bede B., Coroianu L., Gal S.G., Approximation and shape preserving properties of the nonlinear Meyer-König and Zeller operator of max-product kind, Numerical Functional Analysis and Optimization, 31(3), 232–253, 2010.
- Bede B., Gal S.G., Approximation by nonlinear Bernstein and Favard-Szász-Mirakjan operators of max-product kind, Journal of Concrete and Applicable Mathematics, 8(2), 193–207, 2010.
- Bede B., Nobuhara H., Fodor J., Hirota K., Max-product shepard approximation operators, Journal of Advanced Computational Intelligence and Intelligent Informatics, 10, 494–497, 2006.
- Bede B., Coroianu L., Gal S.G., Approximation and shape preserving properties of the nonlinear Bleimann-Butzer-Hahn operators of max-product kind, Commentationes Mathematicae Universitatis Carolinae, 51(3), 397–415, 2010.
- Holhoş A., Weighted approximation of functions by Meyer-König and Zeller operators of max-product type, Numerical Functional Analysis and Optimization, 39(6), 689–703, 2018.
- Güngör Ş.Y., İspir N., Approximation by Bernstein-Chlodowsky operators of max-product kind, Mathematical Communications, 23, 205–225, 2018.
- Rao N., Wafi A., (p,q)-Bivariate-Bernstein-Chlodowsky operators, Filomat, 32(2), 369–378, 2018.
- Raiz M., Rao N., Mishra V.N., Szasz-Type Operators Involving q-Appell Polynomials, Approximation Theory, Sequence Spaces and Applications Industrial and Applied Mathematics, Springer, Singapore, 2022.
- Mishra L.N., Pandey S., Mishra V.N., King type generalization of Baskakov operators based on (p,q) calculus with better approximation properties, Analysis, 40(4), 163–173, 2020.
- Gairola A.R., Singh A., Rathour L., Mishra V.N., Improved rate of approximation by modification of Baskakov operator, Operators and Matrices, 16(4), 1097–1123, 2022.
- Mishra V.N., Raiz M., Rao N., Dunkl analouge of Szász Schurer Beta bivariate operators, Mathematical Foundations of Computing, 6(4), 651–669, 2023.
- Rao N., Heshamuddin M., Shadab M., Srivastava A., Approximation properties of bivariate Szasz Durrmeyer operators via Dunkl analogue, Filomat, 35(13), 4515–4532, 2021.
- 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, 1–11, 2013.
- Mishra L.N., Pandey S., Mishra V.N., On a class of generalised (p,q) Bernstein operators, Indian Journal of Industrial and Applied Mathematics, 10(1), 220–233, 2019.
- Mishra V.N., Pandey S., On (p,q) Baskakov-Durrmeyer-Stancu operators, Advances in Applied Clifford Algebras, 27(2), 1633–1646, 2017.
- Khatri K., Mishra V.N., Generalized Szasz-Mirakyan operators involving Brenke type polynomials, Applied Mathematics and Computation, 324, 228–238, 2018.
DOI: https://doi.org/10.2478/ijmce-2024-0016 | Journal eISSN: 2956-7068
Language: English
Page range: 211 - 222
Submitted on: Jun 13, 2023
Accepted on: Oct 26, 2023
Published on: Jan 10, 2024
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
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© 2024 Ecem Acar, Özge Özalp Güller, Sevilay Kırcı Serenbay, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.