Approximation by nonlinear Meyer-König and Zeller operators based on q-integers

[1] Gupta V., Rassias M.T., Moments of Linear Positive Operators and Approximation, Springer, 2019. GuptaV. RassiasM.T. Moments of Linear Positive Operators and Approximation Springer 2019 Search in Google Scholar

[2] Gal S.G., Shape-Preserving Approximation by Real and Complex Polynomials, Birkhäuser, Boston, 2008. GalS.G. Shape-Preserving Approximation by Real and Complex Polynomials Birkhäuser Boston 2008 Search in Google Scholar

[3] Lupaş A., A q-analogue of the Bernstein operator, Seminar on Numerical and Statistical Calculus, University of Cluj-Napoca, 9, 85–92, 1987. LupaşA. A q-analogue of the Bernstein operator Seminar on Numerical and Statistical Calculus, University of Cluj-Napoca 9 85 92 1987 Search in Google Scholar

[4] Phillips G.M., Bernstein polynomials based on the q-integers, Annals of Numerical Mathematics, 4(1–4), 511–518, 1997. PhillipsG.M. Bernstein polynomials based on the q-integers Annals of Numerical Mathematics 4 1–4 511 518 1997 Search in Google Scholar

[5] Phillips G.M., A generalization of the Bernstein polynomials based on the q-integers, The Anziam Journal, 42(1), 79–86, 2000. PhillipsG.M. A generalization of the Bernstein polynomials based on the q-integers The Anziam Journal 42 1 79 86 2000 Search in Google Scholar

[6] Oruç H., Tuncer N., On the convergence and iterates of q-Bernstein polynomials, Journal of Approximation Theory, 117(2), 301–313, 2002. OruçH. TuncerN. On the convergence and iterates of q-Bernstein polynomials Journal of Approximation Theory 117 2 301 313 2002 Search in Google Scholar

[7] Ostrovska S., q-Bernstein polynomials and their iterates, Journal of Approximation Theory, 123(2), 232–255, 2003. OstrovskaS. q-Bernstein polynomials and their iterates Journal of Approximation Theory 123 2 232 255 2003 Search in Google Scholar

[8] Derriennic M.M., Modified Bernstein polynomials and Jacobi polynomials in q-calculus, Rendiconti del Circolo Matematico di Palermo, 2(76), 269–290, 2005. DerriennicM.M. Modified Bernstein polynomials and Jacobi polynomials in q-calculus Rendiconti del Circolo Matematico di Palermo 2 76 269 290 2005 Search in Google Scholar

[9] Finta Z., Gupta V., Approximation by q-Durrmeyer operators, Journal of Applied Mathematics and Computing, 29, 401–415, 2009. FintaZ. GuptaV. Approximation by q-Durrmeyer operators Journal of Applied Mathematics and Computing 29 401 415 2009 Search in Google Scholar

[10] 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. KhanK. LobiyalD.K. Bèzier curves based on Lupaş (p,q)-analogue of Bernstein functions in CAGD Journal of Computational and Applied Mathematics 317 458 477 2017 Search in Google Scholar

[11] 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. KhanK. LobiyalD.K. KilicmanA. Bèzier curves and surfaces based on modified Bernstein polynomials Azerbaijan Journal of Mathematics 9 1 3 21 2019 Search in Google Scholar

[12] Farouki R.T., The Bernstein polynomial basis: A centennial retrospective, Computer Aided Geometric Design, 29(6), 379–419, 2012. FaroukiR.T. The Bernstein polynomial basis: A centennial retrospective Computer Aided Geometric Design 29 6 379 419 2012 Search in Google Scholar

[13] 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. BedeB. CoroianuL. GalS.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 Search in Google Scholar

[14] 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. AcarE. KarahanD. Kırcı SerenbayS. Approximation for the Bernstein operator of max-product kind in symmetric range Khayyam Journal of Mathematics 6 2 257 273 2020 Search in Google Scholar

[15] 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 GüllerÖ. AcarE. Kırcı SerenbayS. Nonlinear bivariate Bernstein-Chlodowsky operators of maximum product type Journal of Mathematics 2022(ID:4742433), 11 pages, 2022 Search in Google Scholar

[16] 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. Özalp GüllerÖ. AcarE. Kırcı SerenbayS. 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 Search in Google Scholar

[17] 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. BedeB. CoroianuL. GalS.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 Search in Google Scholar

[18] 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. BedeB. GalS.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 Search in Google Scholar

[19] 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. BedeB. NobuharaH. FodorJ. HirotaK. Max-product shepard approximation operators Journal of Advanced Computational Intelligence and Intelligent Informatics 10 494 497 2006 Search in Google Scholar

[20] 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. BedeB. CoroianuL. GalS.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 Search in Google Scholar

[21] 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. HolhoşA. Weighted approximation of functions by Meyer-König and Zeller operators of max-product type Numerical Functional Analysis and Optimization 39 6 689 703 2018 Search in Google Scholar

[22] Güngör Ş.Y., İspir N., Approximation by Bernstein-Chlodowsky operators of max-product kind, Mathematical Communications, 23, 205–225, 2018. GüngörŞ.Y. İspirN. Approximation by Bernstein-Chlodowsky operators of max-product kind Mathematical Communications 23 205 225 2018 Search in Google Scholar

[23] Rao N., Wafi A., (p,q)-Bivariate-Bernstein-Chlodowsky operators, Filomat, 32(2), 369–378, 2018. RaoN. WafiA. (p,q)-Bivariate-Bernstein-Chlodowsky operators Filomat 32 2 369 378 2018 Search in Google Scholar

[24] 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. RaizM. RaoN. MishraV.N. Szasz-Type Operators Involving q-Appell Polynomials, Approximation Theory, Sequence Spaces and Applications Industrial and Applied Mathematics Springer Singapore 2022 Search in Google Scholar

[25] 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. MishraL.N. PandeyS. MishraV.N. King type generalization of Baskakov operators based on (p,q) calculus with better approximation properties Analysis 40 4 163 173 2020 Search in Google Scholar

[26] 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. GairolaA.R. SinghA. RathourL. MishraV.N. Improved rate of approximation by modification of Baskakov operator Operators and Matrices 16 4 1097 1123 2022 Search in Google Scholar

[27] Mishra V.N., Raiz M., Rao N., Dunkl analouge of Szász Schurer Beta bivariate operators, Mathematical Foundations of Computing, 6(4), 651–669, 2023. MishraV.N. RaizM. RaoN. Dunkl analouge of Szász Schurer Beta bivariate operators Mathematical Foundations of Computing 6 4 651 669 2023 Search in Google Scholar

[28] Rao N., Heshamuddin M., Shadab M., Srivastava A., Approximation properties of bivariate Szasz Durrmeyer operators via Dunkl analogue, Filomat, 35(13), 4515–4532, 2021. RaoN. HeshamuddinM. ShadabM. SrivastavaA. Approximation properties of bivariate Szasz Durrmeyer operators via Dunkl analogue Filomat 35 13 4515 4532 2021 Search in Google Scholar

[29] 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. MishraV.N. KhatriK. MishraL.N. Deepmala, Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators Journal of Inequalities and Applications 586 1 11 2013 Search in Google Scholar

[30] 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. MishraL.N. PandeyS. MishraV.N. On a class of generalised (p,q) Bernstein operators Indian Journal of Industrial and Applied Mathematics 10 1 220 233 2019 Search in Google Scholar

[31] Mishra V.N., Pandey S., On (p,q) Baskakov-Durrmeyer-Stancu operators, Advances in Applied Clifford Algebras, 27(2), 1633–1646, 2017. MishraV.N. PandeyS. On (p,q) Baskakov-Durrmeyer-Stancu operators Advances in Applied Clifford Algebras 27 2 1633 1646 2017 Search in Google Scholar

[32] Khatri K., Mishra V.N., Generalized Szasz-Mirakyan operators involving Brenke type polynomials, Applied Mathematics and Computation, 324, 228–238, 2018. KhatriK. MishraV.N. Generalized Szasz-Mirakyan operators involving Brenke type polynomials Applied Mathematics and Computation 324 228 238 2018 Search in Google Scholar